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Polynomial Decay of Correlations for Flows, Including Lorentz Gas Examples

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Abstract

We prove sharp results on polynomial decay of correlations for nonuniformly hyperbolic flows. Applications include intermittent solenoidal flows and various Lorentz gas models including the infinite horizon Lorentz gas.

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Acknowledgements

The research of PB was supported in part by Hungarian National Foundation for Scientific Research (NKFIH OTKA) Grants K104745 and K123782. OB was supported in part by EU Marie-Curie IRSES Brazilian-European partnership in Dynamical Systems (FP7-PEOPLE-2012-IRSES 318999 BREUDS). The research of IM was supported in part by a European Advanced Grant StochExtHomog (ERC AdG 320977). We are grateful to the referees for very helpful comments which led to many clarifications and corrections.

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Authors and Affiliations

  1. MTA-BME Stochastics Research Group, Budapest University of Technology and Economics, Egry József u. 1, Budapest, 1111, Hungary

    Péter Bálint

  2. Department of Stochastics, Budapest University of Technology and Economics, Egry József u. 1, Budapest, 1111, Hungary

    Péter Bálint

  3. University of Nova Gorica, Glavni trg 8, 5271, Vipava, Slovenia

    Oliver Butterley

  4. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

    Ian Melbourne

Authors
  1. Péter Bálint
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  2. Oliver Butterley
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  3. Ian Melbourne
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Correspondence to Ian Melbourne.

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Communicated by C. Liverani

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Bálint, P., Butterley, O. & Melbourne, I. Polynomial Decay of Correlations for Flows, Including Lorentz Gas Examples. Commun. Math. Phys. 368, 55–111 (2019). https://doi.org/10.1007/s00220-019-03423-6

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  • DOI: https://doi.org/10.1007/s00220-019-03423-6

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