Volume 22, issue 3 (2018)

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Counting problem on wind-tree models

Angel Pardo

Geometry & Topology 22 (2018) 1483–1536
Abstract

We study periodic wind-tree models, that is, billiards in the plane endowed with 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 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.

Keywords
billiards, translations surfaces, periodic orbits, counting problem, Siegel–Veech constants
Mathematical Subject Classification 2010
Primary: 37D50, 37C35
Secondary: 30F30, 37A40, 37D40
References
Publication
Received: 23 May 2016
Revised: 23 January 2017
Accepted: 15 May 2017
Published: 16 March 2018
Proposed: Danny Calegari
Seconded: Anna Wienhard, Leonid Polterovich
Authors
Angel Pardo
Institut de Mathématiques de Marseille
Aix-Marseille Université
Marseille
France