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Some statistical properties of almost Anosov diffeomorphisms

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  • Zhang, Xu

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.

Suggested Citation

  • Zhang, Xu, 2019. "Some statistical properties of almost Anosov diffeomorphisms," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 149-162.
    • Handle: RePEc:eee:chsofr:v:123:y:2019:i:c:p:149-162
    DOI: 10.1016/j.chaos.2019.04.005
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