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Equidistribution for Standard Pairs in Planar Dispersing Billiard Flows

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Abstract

We prove exponential correlation decay in dispersing billiard flows on the 2-torus assuming finite horizon and lack of corner points. With applications aimed at describing heat conduction, the highly singular initial measures are concentrated here on 1-dimensional submanifolds (given by standard pairs) and the observables are supposed to satisfy a generalized Hölder continuity property. The result is based on the exponential correlation decay bound of Baladi et al. (Invent Math, 211:39–117, 2018. https://doi.org/10.1007/s00222-017-0745-1) obtained for Hölder continuous observables in these billiards. The model dependence of the bounds is also discussed.

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Authors and Affiliations

  1. Institute of Mathematics, Budapest University of Technology and Economics, Egry József u. 1, Budapest, 1111, Hungary

    Péter Bálint, Domokos Szász & Imre Péter Tóth

  2. MTA-BME Stochastics Research Group, Egry József u. 1, Budapest, 1111, Hungary

    Péter Bálint & Imre Péter Tóth

  3. Department of Mathematics, University of Maryland, 4176 Campus Drive, College Park, MD, 20742, USA

    Péter Nándori

Authors
  1. Péter Bálint
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  2. Péter Nándori
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  3. Domokos Szász
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  4. Imre Péter Tóth
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Correspondence to Péter Bálint.

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Communicated by Dmitry Dolgopyat.

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Bálint, P., Nándori, P., Szász, D. et al. Equidistribution for Standard Pairs in Planar Dispersing Billiard Flows. Ann. Henri Poincaré 19, 979–1042 (2018). https://doi.org/10.1007/s00023-018-0648-8

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  • DOI: https://doi.org/10.1007/s00023-018-0648-8

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