Divergent trajectories in the periodic wind-tree model

Vincent Delecroix

doi:10.3934/jmd.2013.7.1

Article Contents

2013, Volume 7, Issue 1: 1-29. Doi: 10.3934/jmd.2013.7.1

This issue Previous Article Next Article Growth of periodic orbits and generalized diagonals for typical triangular billiards

Divergent trajectories in the periodic wind-tree model

Vincent Delecroix^1,

1.
Université Paris 7, Département de Mathématiques, Bâtiment Sophie Germain, 8 Place FM/13, 75013 Paris

Received: April 2012

Published: May 2013

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Abstract

The periodic wind-tree model is a family $T(a,b)$ of billiards in the plane in which identical rectangular scatterers of size $a \times b$ are disposed periodically at each integer point. In that model, the recurrence is generic with respect to the parameters $a$, $b$, and the angle $\theta$ of initial direction of the particule. In contrast, we prove that for some parameters $(a,b)$ the set of angles $\theta$ for which the billiard flow is divergent has Hausdorff dimension greater than one half.

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Mathematics Subject Classification: Primary: 37B05, 37B10.

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