A Lipschitz Version of the λ-Lemma and a Characterization of Homoclinic and Heteroclinic Orbits

被引：0

作者：

Pires, Leonardo ^{[1
]}

La Guardia, Giuliano G. ^{[1
]}

机构：

[1] Univ Estadual Ponta Grossa, Dept Matemat & Estatast, BR-84030900 Ponta Grossa, Parana, Brazil

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2021年 / 20卷 / 03期

关键词：

Chaos; lambda-Lemma; Lipschitz function; Morse-Smale Lipschitz functions;

D O I：

10.1007/s12346-021-00521-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 finite dimensional framework with a norm between C-1-norm and C-0-norm. As an application, we study homoclinic and heteroclinic orbits obtaining, as a consequence, a stability result for Lipschitz Morse-Smale functions.

引用

页数：15

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