Abstract

We study periodic wind-tree models, that is, billiards in the plane endowed with Z(2)-periodically located identical connected symmetric right-angled obstacles. We give asymptotic formulas for the number of (isotopy classes of) closed billiard trajectories (up to Z(2)-translations) on the wind-tree billiard. We also explicitly compute the associated Siegel-Veech constant for generic wind-tree billiards depending on the number of corners on the obstacle.