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

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

2009-12-15

arxiv.org/abs/0912.2891v1

Journal f\"ur die Reine und Angewandte Mathematik 656 (2011) 223-244

Mathematics

Dynamical Systems

Scientific paper

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 $G_\delta$ of parameters.

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