Type: Article

Billiards in polygons and homogeneous foliations on C^2

Ferrán Valdez;

Abstract:

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 dynamics of the billiard ball is linked to the directional flow of the complex vector field defining the associated holomorphic foliation.