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Licensed Unlicensed Requires Authentication Published by De Gruyter March 15, 2011

The Ehrenfest wind-tree model: periodic directions, recurrence, diffusion

  • Pascal Hubert EMAIL logo , Samuel Lelièvre and Serge Troubetzkoy


We study periodic wind-tree models, unbounded planar billiards with periodically located rectangular obstacles. For a class of rational parameters we show the existence of completely periodic directions, and recurrence; for another class of rational parameters, there are directions in which all trajectories escape, and we prove a rate of escape for almost all directions. These results extend to a dense Gδ of parameters.

Received: 2009-10-09
Revised: 2010-03-15
Published Online: 2011-03-15
Published in Print: 2011-July

© Walter de Gruyter Berlin · New York 2011

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