Transversal periodic-to-periodic homoclinic orbits in singularly perturbed systems
Resource
Discrete and Continuous Dynamical Systems - Series B, 14(2), 367-387
Journal
Discrete and Continuous Dynamical Systems - Series B
Journal Volume
14
Journal Issue
2
Pages
367-387
Date Issued
2010
Date
2010
Author(s)
Battelli, Flaviano
Palmer, Ken
Abstract
We consider a singularly perturbed system with a normally hyperbolic centre manifold. Assuming the existence of a fast homoclinic orbit to a point of the centre manifold belonging to a hyperbolic periodic solution for the slow system, we prove an old and a new result concerning the existence of solutions of the singularly perturbed system that are homoclinic to a periodic solution of the system on the centre manifold. We also give examples in dimensions greater than three of Sil'nikov [16] periodic-to-periodic homoclinic orbits.
Type
journal article