STATISTICAL PROPERTIES OF DIFFEOMORPHISMS WITH WEAK INVARIANT MANIFOLDS

• Type: Article in International Scientific Journal
• Date: 2016

Authors

alves, jf (Author) FCUP; Azevedo, D (Author) Other

Journal

Title: Discrete and Continuous Dynamical Systems

Vol. 36

Pages: 1-41

ISSN: 1078-0947

Publisher: American Institute of Mathematical Sciences

Indexing

ISI Web of Knowledge - 9 Citations

Scopus - 10 Citations

Other information

Authenticus ID: P-00G-NP4

DOI: 10.3934/dcds.2016.36.1

Abstract (EN): We consider diffeomorphisms of compact Riemmanian manifolds which have a Gibbs-Markov-Young structure, consisting of a reference set A with a hyperbolic product structure and a countable Markov partition. We assume polynomial contraction on stable leaves, polynomial backward contraction on unstable leaves, a bounded distortion property and a certain regularity of the stable foliation. We establish a control on the decay of correlations and large deviations of the physical measure of the dynamical system, based on a polynomial control on the Lebesgue measure of the tail of return times. Finally, we present an example of a dynamical system defined on the torus and prove that it verifies the properties of the Gibbs-Markov-Young structure that we considered.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 41