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Dispersing Billiards with Moving Scatterers

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Abstract

We propose a model of Sinai billiards with moving scatterers, in which the locations and shapes of the scatterers may change by small amounts between collisions. Our main result is the exponential loss of memory of initial data at uniform rates, and our proof consists of a coupling argument for non-stationary compositions of maps similar to classical billiard maps. This can be seen as a prototypical result on the statistical properties of time-dependent dynamical systems.

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Authors and Affiliations

  1. Department of Mathematics, University of Rome “Tor Vergata”, Via della Ricerca Scientifica, 00133, Roma, Italy

    Mikko Stenlund

  2. Department of Mathematics and Statistics, University of Helsinki, P. O. Box 68, Helsinki, 00014, Finland

    Mikko Stenlund

  3. Courant Institute of Mathematical Sciences, New York, NY, 10012, USA

    Lai-Sang Young

  4. Department of Mathematics & Statistics, University of Massachusetts, Amherst, 01003, USA

    Hongkun Zhang

Authors
  1. Mikko Stenlund
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  2. Lai-Sang Young
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  3. Hongkun Zhang
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Correspondence to Mikko Stenlund.

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Communicated by G. Gallavotti

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Stenlund, M., Young, LS. & Zhang, H. Dispersing Billiards with Moving Scatterers. Commun. Math. Phys. 322, 909–955 (2013). https://doi.org/10.1007/s00220-013-1746-6

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  • DOI: https://doi.org/10.1007/s00220-013-1746-6

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