We study periodic wind-tree models, that is, billiards in the plane endowed with –periodically located identical connected symmetric right-angled obstacles. We give asymptotic formulas for the number of (isotopy classes of) closed billiard trajectories (up to –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.
"Counting problem on wind-tree models." Geom. Topol. 22 (3) 1483 - 1536, 2018. https://doi.org/10.2140/gt.2018.22.1483