Global Effect of Non-Conservative Perturbations on Homoclinic Orbits

Gidea Marian ^[1] ; de la Llave Rafael ^[2] ; Musser, Maxwell ^[1]
1. [1] Yeshiva University
  
  Yeshiva University
  
  Estados Unidos
2. [2] Georgia Institute of Technology
  
  Georgia Institute of Technology
  
  Estados Unidos
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 1, 2021
Idioma: inglés
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Resumen
- 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 its 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 for perturbations of both uncoupled and coupled rotator-pendulum systems.