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.

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

References in corpus (4)

• Invariant and stationary measures for the SL(2,R) action on Moduli space
• Right-angled billiards and volumes of moduli spaces of quadratic differentials on $\mathbb{C}{P}^1$
• Cries and whispers in wind-tree forests
• Configurations of saddle connections of quadratic differentials on CP1 and on hyperelliptic Riemann surfaces

Cited by in corpus (1)

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