The NHIM development scenario in an asymmetric binary system of dwarf galaxies

Abstract: We study the development scenario of a three-degree-of-freedom Hamiltonian system.We observe how the fundamental normally hyperbolic invariant manifolds (NHIMs) form a homoclinic/heteroclinic tangle. As the energy increases, the NHIMs begin to lose normal hyperbolicity and decay, creating tangential transient effects. We also observe a certain kind of coordination between the development scenarios of these NHIMs. We analyse this phenomenon using Poincar\'e maps and phase space indicator functions. As an example of demonstration, we use a relatively simple model of a test particle moving in the gravitational field of a pair of interacting dwarf galaxies.