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Caputo Fractional Standard Map: Scaling Invariance Analyses (2312.00524v2)
Published 1 Dec 2023 in nlin.CD
Abstract: In this paper, we investigate the scaling invariance of survival probability in the Caputo fractional standard map of the order $1<\alpha<2$ considered on a cylinder. We consider relatively large values of the nonlinearity parameter $K$ for which the map is chaotic. The survival probability has a short plateau followed by an exponential decay and is scaling invariant for all considered values of $\alpha$ and $K$.
- V.E. Tarasov Differential equations with fractional derivative and universal map with memory, J. Phys. A 42 (2009) 465102. DOI: https://doi.org/10.1088/1751-8113/42/46/465102
- V.E. Tarasov, G.M. Zaslavsky, “Fractional equations of kicked systems and discrete maps”, Journal of Physics A 41(43), (2008) 435101. DOI: https://doi.org/10.1088/1751-8113/42/46/465102
- M. Edelman, “Fractional Standard Map: Riemann-Liouville vs. Caputo”, Commun. Nonlin. Sci. Numer. Simul. 16, 4573-4580 (2011). DOI: https://doi.org/10.1016/j.cnsns.2011.02.007
- M. Edelman, “Fractional Maps and Fractional Attractors. Part I: α𝛼\alphaitalic_α-Families of Maps”, Discontinuity, Nonlinearity, and Complexity 1, 305-324, (2013). DOI: https://doi.org/10.5890/DNC.2015.11.003
- M. Edelman and L.A. Taieb, “New types of solutions of non-linear fractional differential equations”, in: Advances in Harmonic Analysis and Operator Theory; Series: Operator Theory: Advances and Applications, A. Almeida, L. Castro, F.-O. Speck (Eds.) pp. 139-155 (Springer, Basel, 2013); arXiv:1211.4012.
- M. Edelman, “Universality in Systems with Power-Law Memory and Fractional Dynamics”, in: M. Edelman, E. Macau, and M. A. F. Sanjuan (eds.): Chaotic, Fractional, and Complex Dynamics: New Insights and Perspectives; Series: Understanding Complex Systems, 147–171, Springer, eBook, 2018.
- M. Edelman, “Dynamics of nonlinear systems with power-law memory” in V.E. Tarasov (ed.), Handbook of Fractional Calculus with Applications, Volume 4, Applications in Physics, p. 103-132, De Gruyter, Berlin, 2019
- M. Edelman and A. B. Helman, “Asymptotic cycles in fractional maps of arbitrary positive orders”, Fract. Calc. Appl. Anal. (2022). https://doi.org/10.1007/s13540-021-00008-w
- G.M. Zaslavsky, M. Edelman, and B.A. Niyazov, “Self-Similarity, Renormalization, and Phase Space Nonuniformity of Hamiltonian Chaotic Dynamics”, Chaos 7, 159-181 (1997). DOI: https://doi.org/10.1063/1.166252