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

• Pires, Leonardo ^[1] ; La Guardia, Giuliano G. ^[1]
  1. [1] Universidade Estadual de Ponta Grossa

     Universidade Estadual de Ponta Grossa

     Brasil

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 3, 2021
• Idioma: inglés
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• Resumen

  • 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.