Uniform hyperbolicity revisited: index of periodic points and equidimensional cycles

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

Autores

Bessa, M (Autor) Outra; Jorge Rocha (Autor) FCUP; Varandas, P (Autor) FCUP

Revista

Título: Dynamical Systems

Vol. 33

Páginas: 691-707

ISSN: 1468-9367

Editora: Taylor & Francis

Indexação

ISI Web of Knowledge - 1 Citação

Scopus - 1 Citação

Outras Informações

ID Authenticus: P-00P-VCG

DOI: 10.1080/14689367.2018.1433818

Abstract (EN): In this paper, we revisit uniformly hyperbolic basic sets and the domination of Oseledets splittings at periodic points. We prove that periodic points with simple Lyapunov spectrum are dense in non-trivial basic pieces of C-r-residual diffeomorphisms on three-dimensional manifolds (r 1). In the case of the C-1-topology, we can prove that either all periodic points of a hyperbolic basic piece for a diffeomorphism f have simple spectrum C-1-robustly (in which case f has a finest dominated splitting into one-dimensional sub-bundles and all Lyapunov exponent functions of f are continuous in the weak(*)-topology) or it can be C-1-approximated by an equidimensional cycle associated to periodic points with robust different signatures. The latter can be used as a mechanism to guarantee the coexistence of infinitely many periodic points with different signatures.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 17