Uniform hyperbolicity revisited: index of periodic points and equidimensional cycles

• Type: Article in International Scientific Journal
• Date: 2018

Authors

Bessa, M (Author) Other; Jorge Rocha (Author) FCUP; Varandas, P (Author) FCUP

Journal

Title: Dynamical Systems

Vol. 33

Pages: 691-707

ISSN: 1468-9367

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 17