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On Statistical Properties of Hyperbolic Systems with Singularities

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Abstract

We study hyperbolic systems with singularities and prove the coupling lemma and exponential decay of correlations under weaker assumptions than previously adopted in similar studies. Our new approach allows us to study the mixing rates of the reduced map for certain billiard models that could not be handled by the traditional techniques. These models include modified Bunimovich stadia, which are bounded by minor arcs, and flower-type regions that are bounded by major arcs.

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Authors and Affiliations

  1. Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL, 35294, USA

    Nikolai Chernov

  2. Department of Math. & Statis., University of Massachusetts, Amherst, MA, 01003, USA

    Hong-Kun Zhang

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  1. Nikolai Chernov
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  2. Hong-Kun Zhang
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Correspondence to Hong-Kun Zhang.

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Chernov, N., Zhang, HK. On Statistical Properties of Hyperbolic Systems with Singularities. J Stat Phys 136, 615–642 (2009). https://doi.org/10.1007/s10955-009-9804-3

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  • DOI: https://doi.org/10.1007/s10955-009-9804-3

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