The NHIM bifurcation scenario of a particle in an asymmetric binary system of dwarf galaxies

TL;DR

This paper investigates the bifurcation behavior of a Hamiltonian system modeling a particle influenced by two dwarf galaxies, revealing how NHIMs lose hyperbolicity and induce chaotic dynamics as parameters change.

Contribution

It introduces a detailed analysis of NHIM bifurcations in a three-degree-of-freedom gravitational model, highlighting the coordination between bifurcation scenarios and chaos onset.

Findings

NHIMs lose normal hyperbolicity with increasing perturbation

KAM tori break leading to transient chaos

Coordination observed between bifurcation scenarios of NHIMs

Abstract

We study the bifurcation scenario of a three-degree-of-freedom Hamiltonian system, a model based on the Lagrange restricted 3-body problem: a test particle moving in the gravitational field of a pair of interacting dwarf galaxies. The phase space of this system has 3 fundamental normally hyperbolic invariant manifolds (NHIMs) and their invariant stable and unstable manifolds form homoclinic/heteroclinic tangles. As the perturbation parameter increases, the NHIMs begin to lose normal hyperbolicity and their constituent KAM tori break, creating transient chaotic dynamics around them. We also observe a certain kind of coordination between the bifurcation scenarios of these NHIMs. We analyse this phenomenon using Poincar\'e maps and the delay time function.