Some statistical properties of almost Anosov diffeomorphisms

Xu Zhang

Chaos, Solitons & Fractals, 2019, vol. 123, issue C, 149-162

Abstract: For a kind of almost Anosov diffeomorphisms, we study the relationship among the existence of Sinai-Ruelle-Bowen (SRB) measures, the local differentiability near the indifferent fixed points, and space dimension, where the almost Anosov diffeomorphisms are hyperbolic everywhere except for the indifferent fixed points. As a consequence, there are C2 almost Anosov diffeomorphisms that admit σ-finite (infinite) SRB measures in spaces with dimensions bigger than one; there exist C2 almost Anosov diffeomorphisms with finite SRB measures in spaces with dimensions bigger than three. Further, we obtain the lower and upper polynomial bounds for the decay rates of the correlation functions of the Hölder observables for the maps admitting finite SRB measures.

Keywords: Almost Anosov diffeomorphism; Correlation function; Decay rate; Sinai-Ruelle-Bowen measure (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:123:y:2019:i:c:p:149-162

DOI: 10.1016/j.chaos.2019.04.005

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