English

A Lipschitz version of the $\lambda$-Lemma and a characterization of homoclinic and heteroclinic orbits

Analysis of PDEs 2021-09-16 v4 Dynamical Systems

Abstract

In this paper we consider finite dimensional dynamical systems generated by a Lipschitz function. We prove a version of the Whitney's Extension Theorem on compact manifolds to obtain a version of the well-known Lambda Lemma for Lipschitz functions. The notions of Lipschitz transversality and hyperbolicity are investigated in the context of finite dimension with a norm weaker than C1C^1-norm and stronger than C0C^0-norm.

Keywords

Cite

@article{arxiv.2002.06615,
  title  = {A Lipschitz version of the $\lambda$-Lemma and a characterization of homoclinic and heteroclinic orbits},
  author = {Leonardo Pires and Giuliano G. La Guardia},
  journal= {arXiv preprint arXiv:2002.06615},
  year   = {2021}
}