Divergent trajectories in the periodic wind-tree model
Vincent Delecroix - Université Paris 7, Département de Mathématiques, Bâtiment Sophie Germain, 8 Place FM/13, 75013 Paris, France (email)
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.
Keywords: Wind-tree model, rational billiard, interval-exchange transformations.
Received: April 2012; Published: May 2013.