Gibbs-Markov-Young structures with (stretched) exponential tail for partially hyperbolic attractors

• Type: Article in International Scientific Journal
• Date: 2015

Authors

alves, jf (Author) FCUP; Li, X (Author) Other

Journal

Title: Advances in Mathematics

Vol. 279

Pages: 405-437

ISSN: 0001-8708

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 8 Citations

Scopus - 13 Citations

Other information

Authenticus ID: P-00A-CHW

DOI: 10.1016/j.aim.2015.02.017

Abstract (EN): In this work we extend the results obtained by Gouezel in [12] to partially hyperbolic attractors. We study a forward invariant set K on a Riemannian manifold M whose tangent space splits as dominated decomposition TKM = E-cu circle plus E-s, for which the center-unstable direction E-cu is non-uniformly expanding on some local unstable disk. We prove that the (stretched) exponential decay of recurrence times for an induced scheme can be deduced under the assumption of (stretched) exponential decay of the time that typical points need to achieve some uniform expanding in the center-unstable direction. As an application of our results we obtain exponential decay of correlations and exponential large deviations for a class of partially hyperbolic diffeomorphisms considered in [1].

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 33