Gibbs-Markov structures and limit laws for partially hyperbolic attractors with mostly expanding central direction

• Type: Article in International Scientific Journal
• Date: 2010

Authors

alves, jf (Author) FCUP; pinheiro, v (Author) Other

Journal

Title: Advances in Mathematics

Vol. 223

Pages: 1706-1730

ISSN: 0001-8708

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 11 Citations

Scopus - 14 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-003-884

DOI: 10.1016/j.aim.2009.10.010

Abstract (EN): We consider a partially hyperbolic set K on a Riemannian manifold M whose tangent space splits as T(K)M = E(cu) circle plus E(s), for which the center-unstable direction E(cu) expands non-uniformly on some local unstable disk. We show that under these assumptions f induces a Gibbs-Markov structure. Moreover, the decay of the return time function can be controlled in terms of the time typical points need to achieve some uniform expanding behavior in the center-unstable direction. As an application of the main result we obtain certain rates for decay of correlations, large deviations, an almost sure invariance principle and the validity of the central limit theorem.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 25