Counting problem on wind-tree models

Abstract

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

arXiv comment41 pages, 15 figures. arXiv admin note: substantial text overlap with arXiv:1502.06405 by other authors

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Cited by in corpus (1)

• A non-varying phenomenon with an application to the wind-tree model