2000 character limit reached
Structure of Periodic Orbit Families in the Hill Restricted 4-Body Problem
Published 29 Feb 2024 in math.DS and nlin.CD | (2402.19181v1)
Abstract: The Hill Restricted 4-Body Problem (HR4BP) is a coherent time-periodic model that can be used to represent motion in the Sun-Earth-Moon (SEM) system. Periodic orbits were computed in this model to better understand the periodic orbit family structures that exist in these types of systems. First, periodic orbits in the Circular Restricted 3-Body Problem (CR3BP) representation of the Earth-Moon (EM) system were identified. A Melnikov-type function was used to identify a set of candidate points on the EM CR3BP periodic orbits to start a continuation algorithm. A pseudo-arclength continuation scheme was then used to obtain the corresponding periodic orbit families in the HR4BP when including the effect of the Sun. Bifurcation points were identified in the computed families to obtain additional orbit families.
- NASA Office of the Chief Financial Officer: NASA Strategic Plan 2022. N PD 1001 0D, NASA (Mar 2022) Whitley et al. [2018] Whitley, R.J., Davis, D.C., Burke, L.M., McCarthy, B.P., Power, R.J., Mcguire, M.L., Howell, K.C.: Earth-Moon Near Rectilinear Halo and Butterfly Orbits for Lunar Surface Exploration. In: AAS/AIAA Astrodynamics Conference (2018) Szebehely [1967] Szebehely, V.: Theory of Orbits: The Restricted Problem of Three Bodies. Academic Press Inc (1967) Park and Howell [2022] Park, B., Howell, K.C.: Leveraging Intermediate Dynamical Models for Transitioning from the Circular Restricted Three-Body Problem to an Ephemeris Model. In: AAS/AIAA Astrodynamics Specialist Conference (2022) Peng and Bai [2018] Peng, H., Bai, X.: Natural deep space satellite constellation in the Earth-Moon elliptic system. Acta Astronautica 153, 240–258 (2018) Huang [1960] Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Whitley, R.J., Davis, D.C., Burke, L.M., McCarthy, B.P., Power, R.J., Mcguire, M.L., Howell, K.C.: Earth-Moon Near Rectilinear Halo and Butterfly Orbits for Lunar Surface Exploration. In: AAS/AIAA Astrodynamics Conference (2018) Szebehely [1967] Szebehely, V.: Theory of Orbits: The Restricted Problem of Three Bodies. Academic Press Inc (1967) Park and Howell [2022] Park, B., Howell, K.C.: Leveraging Intermediate Dynamical Models for Transitioning from the Circular Restricted Three-Body Problem to an Ephemeris Model. In: AAS/AIAA Astrodynamics Specialist Conference (2022) Peng and Bai [2018] Peng, H., Bai, X.: Natural deep space satellite constellation in the Earth-Moon elliptic system. Acta Astronautica 153, 240–258 (2018) Huang [1960] Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Szebehely, V.: Theory of Orbits: The Restricted Problem of Three Bodies. Academic Press Inc (1967) Park and Howell [2022] Park, B., Howell, K.C.: Leveraging Intermediate Dynamical Models for Transitioning from the Circular Restricted Three-Body Problem to an Ephemeris Model. In: AAS/AIAA Astrodynamics Specialist Conference (2022) Peng and Bai [2018] Peng, H., Bai, X.: Natural deep space satellite constellation in the Earth-Moon elliptic system. Acta Astronautica 153, 240–258 (2018) Huang [1960] Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Park, B., Howell, K.C.: Leveraging Intermediate Dynamical Models for Transitioning from the Circular Restricted Three-Body Problem to an Ephemeris Model. In: AAS/AIAA Astrodynamics Specialist Conference (2022) Peng and Bai [2018] Peng, H., Bai, X.: Natural deep space satellite constellation in the Earth-Moon elliptic system. Acta Astronautica 153, 240–258 (2018) Huang [1960] Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peng, H., Bai, X.: Natural deep space satellite constellation in the Earth-Moon elliptic system. Acta Astronautica 153, 240–258 (2018) Huang [1960] Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Whitley, R.J., Davis, D.C., Burke, L.M., McCarthy, B.P., Power, R.J., Mcguire, M.L., Howell, K.C.: Earth-Moon Near Rectilinear Halo and Butterfly Orbits for Lunar Surface Exploration. In: AAS/AIAA Astrodynamics Conference (2018) Szebehely [1967] Szebehely, V.: Theory of Orbits: The Restricted Problem of Three Bodies. Academic Press Inc (1967) Park and Howell [2022] Park, B., Howell, K.C.: Leveraging Intermediate Dynamical Models for Transitioning from the Circular Restricted Three-Body Problem to an Ephemeris Model. In: AAS/AIAA Astrodynamics Specialist Conference (2022) Peng and Bai [2018] Peng, H., Bai, X.: Natural deep space satellite constellation in the Earth-Moon elliptic system. Acta Astronautica 153, 240–258 (2018) Huang [1960] Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Szebehely, V.: Theory of Orbits: The Restricted Problem of Three Bodies. Academic Press Inc (1967) Park and Howell [2022] Park, B., Howell, K.C.: Leveraging Intermediate Dynamical Models for Transitioning from the Circular Restricted Three-Body Problem to an Ephemeris Model. In: AAS/AIAA Astrodynamics Specialist Conference (2022) Peng and Bai [2018] Peng, H., Bai, X.: Natural deep space satellite constellation in the Earth-Moon elliptic system. Acta Astronautica 153, 240–258 (2018) Huang [1960] Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Park, B., Howell, K.C.: Leveraging Intermediate Dynamical Models for Transitioning from the Circular Restricted Three-Body Problem to an Ephemeris Model. In: AAS/AIAA Astrodynamics Specialist Conference (2022) Peng and Bai [2018] Peng, H., Bai, X.: Natural deep space satellite constellation in the Earth-Moon elliptic system. Acta Astronautica 153, 240–258 (2018) Huang [1960] Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peng, H., Bai, X.: Natural deep space satellite constellation in the Earth-Moon elliptic system. Acta Astronautica 153, 240–258 (2018) Huang [1960] Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
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Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Park, B., Howell, K.C.: Leveraging Intermediate Dynamical Models for Transitioning from the Circular Restricted Three-Body Problem to an Ephemeris Model. In: AAS/AIAA Astrodynamics Specialist Conference (2022) Peng and Bai [2018] Peng, H., Bai, X.: Natural deep space satellite constellation in the Earth-Moon elliptic system. Acta Astronautica 153, 240–258 (2018) Huang [1960] Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peng, H., Bai, X.: Natural deep space satellite constellation in the Earth-Moon elliptic system. Acta Astronautica 153, 240–258 (2018) Huang [1960] Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Park, B., Howell, K.C.: Leveraging Intermediate Dynamical Models for Transitioning from the Circular Restricted Three-Body Problem to an Ephemeris Model. In: AAS/AIAA Astrodynamics Specialist Conference (2022) Peng and Bai [2018] Peng, H., Bai, X.: Natural deep space satellite constellation in the Earth-Moon elliptic system. Acta Astronautica 153, 240–258 (2018) Huang [1960] Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peng, H., Bai, X.: Natural deep space satellite constellation in the Earth-Moon elliptic system. Acta Astronautica 153, 240–258 (2018) Huang [1960] Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Peng, H., Bai, X.: Natural deep space satellite constellation in the Earth-Moon elliptic system. Acta Astronautica 153, 240–258 (2018) Huang [1960] Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Huang, S.-S.: Very Restricted Four-Body Problem. TN D-501, NASA (Sep 1960) Gómez et al. [2001] Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Gómez, G., Jorba, Á., Masdemont, J., Simó, C.: Normal form of the bicircular model and related topics. In: Dynamics and Mission Design Near Libration Points, pp. 53–110. World Scientific (2001) Rosales [2020] Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Rosales, J.J.: On the effect of the Sun’s gravity around the Earth-Moon L1 and L2 libration points. PhD thesis, Universitat de Barcelona (2020) Jorba-Cuscó et al. [2018] Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Jorba-Cuscó, M., Farrés, A., Jorba, Á.: Two Periodic Models for the Earth-Moon System. Frontiers in Applied Mathematics and Statistics 4 (2018) Simó et al. [1995] Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Simó, C., Gómez, G., Jorba, Á., Masdemont, J.: The Bicircular Model Near the Triangular Libration Points of the RTBP. In: From Newton to Chaos: Modern Techniques for Understanding and Coping with Chaos in N-Body Dynamical Systems, pp. 343–370. Springer (1995) Boudad et al. [2020] Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Boudad, K.K., Howell, K.C., Davis, D.C.: Dynamics of synodic resonant near rectilinear halo orbits in the bicircular four-body problem. Advances in Space Research 66(9), 2194–2214 (2020) Castellá and Jorba [2000] Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Castellá, E., Jorba, Á.: On the vertical families of two-dimensional tori near the triangular points of the Bicircular problem. Celestial Mechanics and Dynamical Astronomy 76, 35–54 (2000) Rosales et al. [2021] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Families of Halo-like invariant tori around L2 in the Earth-Moon Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 133 (2021) Andreu [1998] Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Andreu, M.A.: The Quasi-bicircular Problem. PhD thesis, Universitat de Barcelona (1998) Rosales et al. [2023] Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Rosales, J.J., Jorba, Á., Jorba-Cuscó, M.: Invariant manifolds near L1 and L2 in the quasi-bicircular problem. Celestial Mechanics and Dynamical Astronomy 135 (2023) Scheeres [1998] Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Scheeres, D.J.: The Restricted Hill Four-Body Problem with Applications to the Earth–Moon–Sun System. Celestial Mechanics and Dynamical Astronomy 70(2), 75–98 (1998) Peterson et al. [2023] Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Peterson, L.T., Rosales, J.J., Scheeres, D.J.: The vicinity of Earth–Moon L1 and L2 in the Hill restricted 4-body problem. Physica D: Nonlinear Phenomena 455 (2023) Olikara et al. [2016] Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Olikara, Z.P., Gómez, G., Masdemont, J.J.: A Note on Dynamics About the Coherent Sun-Earth-Moon Collinear Libration Points. In: Gómez, G., Masdemont, J.J. (eds.) Astrodynamics Network AstroNet-II, pp. 183–192. Springer (2016) Henry et al. [2023a] Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Henry, D., Rosales, J., Brown, G., Peterson, L., Scheeres, D.: Quasi-Periodic Orbits near Earth-Moon L1 in the Hill Restricted Four-Body Problem. In: 34th ISTS (2023) Henry et al. [2023b] Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Henry, D.B., Rosales, J., Brown, G.M., Scheeres, D.J.: Quasi-Periodic Orbits near Earth-Moon L1 and L2 in the Hill Restricted Four-Body Problem. In: AAS/AIAA Astrodynamics Specialist Conference (2023) Peterson et al. [2024] Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Peterson, L.T., Jorba, A., Brown, G.M., Scheeres, D.J.: Dynamics Around the Earth-Moon Triangular Points in the Hill Restricted 4-Body Problem. Communications in Nonlinear Science and Numerical Simulation (2024). In Preparation Olikara and Scheeres [2017] Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Olikara, Z.P., Scheeres, D.J.: Mapping Connections Between Planar Sun-Earth-Moon Libration Orbits. In: 27th AAS/AIAA Space Flight Mechanics Meeting (2017) Sanaga and Howell [2023] Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Sanaga, R.R., Howell, K.C.: Synodic Resonant Halo Orbits in the Hill Restricted Four-Body Problem. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023) Melnikov [1963] Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Melnikov, V.K.: On the stability of the center for time periodic perturbations. Transactions of the Moscow Mathematical Society 12, 1–57 (1963) Greenspan and Holmes [1981] Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Greenspan, B.D., Holmes, P.: Homoclinic Orbits, Subharmonics and Global Bifurcations in Forced Oscillations. ADA103564, U.S. Army Research Office (Jun 1981) Wiggins [2003] Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Texts in Applied Mathematics. Springer (2003) Guckenheimer and Holmes [1983] Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Guckenheimer, J., Holmes, P.: Nonlinear Dylanicas, Systems, and Bifurcations of Vector Fields. Applied Mathematical Sciences. Springer (1983) Perko [2001] Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Perko, L.: Differential Equations and Dynamical Systems, 3rd edn. Texts in Applied Mathematics. Springer (2001) Haller [1999] Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Haller, G.: Chaos Near Resonance. Applied Mathematical Sciences. Springer (1999) Guo et al. [2022] Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Guo, X., Tian, R., Xue, Q., Zhang, X.: Sub-harmonic Melnikov function for a high-dimensional non-smooth coupled system. Chaos, Solitons & Fractals 164 (2022) Veerman and Holmes [1985] Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Veerman, P., Holmes, P.: The existence of arbitrarily many distinct periodic orbits in a two degree of freedom hamiltonian system. Physica D: Nonlinear Phenomena 14(2), 177–192 (1985) Yagasaki [1996] Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Yagasaki, K.: The melnikov theory for subharmonics and their bifurcations in forced oscillations. SIAM Journal on Applied Mathematics 56(6), 1720–1765 (1996) Polcar and Semerák [2019] Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Polcar, L., Semerák, O.: Free motion around black holes with discs or rings: Between integrability and chaos. VI. The Melnikov method. Phys. Rev. D 100(10) (2019) Cenedese and Haller [2020] Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Cenedese, M., Haller, G.: How do conservative backbone curves perturb into forced responses? A Melnikov function analysis. Proceedings of the Royal Society A 476(2234) (2020) Rhouma and Chicone [2000] Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Rhouma, M.B.H., Chicone, C.: On the Continuation of Periodic Orbits. Methods and Applications of Analysis 7(1), 85–104 (2000) Scheeres [2012] Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Scheeres, D.J.: Orbital Motion in Strongly Perturbed Environments. Springer (2012) Holmes [1990] Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Holmes, P.: Poincaré, celestial mechanics, dynamical-systems theory and “chaos”. Physics Reports 193(3), 137–163 (1990) Wintner [1952] Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952) Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
- Wintner, A.: The Analytical Foundations of Celestial Mechanics. Dover Books on Physics. Dover Publications (1952)
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