A Lipschitz Version of the $$\lambda $$-Lemma and a Characterization of Homoclinic and Heteroclinic Orbits

Autor:	Giuliano G. La Guardia, Leonardo Pires
Rok vydání:	2021
Předmět:	Lemma (mathematics) Pure mathematics Mathematics::Dynamical Systems Transversality Dynamical systems theory Applied Mathematics Norm (mathematics) Discrete Mathematics and Combinatorics Homoclinic orbit Extension (predicate logic) Characterization (mathematics) Lipschitz continuity Mathematics
Zdroj:	Qualitative Theory of Dynamical Systems. 20
ISSN:	1662-3592 1575-5460
DOI:	10.1007/s12346-021-00521-6
Popis:	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 λ-lemma for Lipschitz functions. The notions of Lipschitz transversality and hyperbolicity are investigated in the finite dimensional framework with a norm between C1-norm and C0-norm. As an application, we study homoclinic and heteroclinic orbits obtaining, as a consequence, a stability result for Lipschitz Morse–Smale functions.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::19e86f74cc48017024e453b174888a14 https://doi.org/10.1007/s12346-021-00521-6 Zobrazit plný text záznamu Full text from SpringerLink