Billiards in polygons and homogeneous foliations on C^2

Ferran Valdez (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this article we construct a new framework for the study of polygonal billiards. To every polygonal billiard we associate a holomorphic foliation on C^2. The dymamics of the billiard ball is linked to the directional flow of the complex vector field defining the associated foliation

Mots clés: Billiards; foliations

Domaines: Systèmes dynamiques [math.DS]

Ferran Valdez. Billiards in polygons and homogeneous foliations on C^2. Ergodic Theory and Dynamical Systems, 2009, 29 (1), pp.255-271. ⟨10.1017/S0143385708000151⟩. ⟨hal-00161994⟩