Global effect of non-conservative perturbations on homoclinic orbits
Dynamical Systems
2019-09-06 v1
Abstract
We study the effect of time-dependent, non-conservative perturbations on the dynamics along homoclinic orbits to a normally hyperbolic invariant manifold. We assume that the unperturbed system is Hamiltonian, and the normally hyperbolic invariant manifold is parametrized via action-angle coordinates. The homoclinic excursions can be described via the scattering map, which gives the future asymptotic of an orbit as a function of the past asymptotic. We provide explicit formulas, in terms of convergent integrals, for the perturbed scattering map expressed in action-angle coordinates. We illustrate these formulas in the case of a perturbed rotator-pendulum system.
Keywords
Cite
@article{arxiv.1909.02080,
title = {Global effect of non-conservative perturbations on homoclinic orbits},
author = {Marian Gidea and Rafael de la Llave and Maxwell Musser},
journal= {arXiv preprint arXiv:1909.02080},
year = {2019}
}