Normally Elliptic Singular Perturbations and Persistence of Homoclinic Orbits
Dynamical Systems
2011-03-10 v1
Abstract
We consider a dynamical system, possibly infinite dimensional or non-autonomous, with fast and slow time scales which is oscillatory with high frequencies in the fast directions. We first derive and justify the limit system of the slow variables. Assuming a steady state persists, we construct the stable, unstable, center-stable, center-unstable, and center manifolds of the steady state of a size of order O(1) and give their leading order approximations. Finally, using these tools, we study the persistence of homoclinic solutions in this type of normally elliptic singular perturbation problems.
Keywords
Cite
@article{arxiv.1012.0079,
title = {Normally Elliptic Singular Perturbations and Persistence of Homoclinic Orbits},
author = {Nan Lu and Chongchun Zeng},
journal= {arXiv preprint arXiv:1012.0079},
year = {2011}
}