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Infinite Ergodic Index of the Ehrenfest Wind-Tree Model

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Abstract

The set of all possible configurations of the Ehrenfest wind-tree model endowed with the Hausdorff topology is a compact metric space. For a typical configuration we show that the wind-tree dynamics has infinite ergodic index in almost every direction. In particular some ergodic theorems can be applied to show that if we start with a large number of initially parallel particles their directions decorrelate as the dynamics evolve, answering the question posed by the Ehrenfests.

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Authors and Affiliations

  1. Inria, 2 rue Simone Iff, 75012, Paris, France

    Alba Málaga Sabogal

  2. Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France

    Serge Eugene Troubetzkoy

  3. I2M, Luminy, Case 907, 13288, Marseille CEDEX 9, France

    Serge Eugene Troubetzkoy

Authors
  1. Alba Málaga Sabogal
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  2. Serge Eugene Troubetzkoy
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Corresponding author

Correspondence to Serge Eugene Troubetzkoy.

Additional information

Communicated by J. Marklof

We thank Jack Milnor for suggesting a nice presentation of our topology. AMS acknowledges that this work was started during a post-doc funded by the A*MIDEX project (ANR-11-IDEX-0001-02), funded itself by the “Investissements d’avenir” program of the French Government, managed by the French National Research Agency (ANR)”. She continued working on this project during the ATER positions she held at the Mathematics Laboratory in Orsay in 2015–2016 and at the THIM-CHArt laboratory in Saint-Denis in 2016–2017. ST gratefully acknowledges the support of project APEX “Systèmes dynamiques: Probabilités et Approximation Diophantienne PAD” funded by the Région PACA.

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Málaga Sabogal, A., Troubetzkoy, S.E. Infinite Ergodic Index of the Ehrenfest Wind-Tree Model. Commun. Math. Phys. 358, 995–1006 (2018). https://doi.org/10.1007/s00220-017-3058-8

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  • DOI: https://doi.org/10.1007/s00220-017-3058-8

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