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arXiv · 1909.02080

Global effect of non-conservative perturbations on homoclinic orbits

Marian Gidea·Rafael de la Llave·Maxwell Musser
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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.

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Marian Gidea, Rafael de la Llave, Maxwell Musser. 2019-09-04. Global effect of non-conservative perturbations on homoclinic orbits. https://arxiv.org/abs/1909.02080

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