On sensitivity to initial conditions and uniqueness of conjugacies for structurally stable diffeomorphisms

• Tipo: Artigo em Revista Científica Internacional
• Data: 2018

Autores

Jorge Rocha (Autor) FCUP; Varandas, P (Autor) FCUP

Revista

Título: Nonlinearity

Vol. 31

Páginas: 293-313

ISSN: 0951-7715

Editora: Institute of Physics Publishing

Indexação

ISI Web of Knowledge - 2 Citações

Scopus - 1 Citação

Outras Informações

ID Authenticus: P-00N-B7T

DOI: 10.1088/1361-6544/aa8d78

Abstract (EN): In this paper we study C-1-structurally stable diffeomorphisms, that is, C-1 Axiom A diffeomorphisms with the strong transversality condition. In contrast to the case of dynamics restricted to a hyperbolic basic piece, structurally stable diffeomorphisms are in general not expansive and the conjugacies between C-1-close structurally stable diffeomorphisms may be non-unique, even if there are assumed C-0-close to the identity. Here we give a necessary and sufficient condition for a structurally stable diffeomorphism to admit a dense subset of points with expansiveness and sensitivity to initial conditions. Morever, we prove that the set of conjugacies between elements in the same conjugacy class is homeomorphic to the C-0-centralizer of the dynamics. Finally, we use this fact to deduce that any two C-1-close structurally stable diffeomorphisms are conjugated by a unique conjugacy C-0-close to the identity if and only if these are Anosov.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 21