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Feuilletages Homogènes et billards polygonaux

Abstract : In this thesis we provide a new framework for the study of polygonal billiards. To every polygonal billiard we associate canonically a holomorphic foliation on the affine complex space of dimension two. The dynamic of the billiard ball is linked to the directional flow of the complex vector field defining this holomorphic foliation. This dictionary leads to a topological description of the translation surfaces naturally associated to the polygonal billiard. Inversely, we use the polygonal billiard to describe a certain class of real foliations on the projective space of dimension three.
Keywords : Billiards foliations
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Contributor : Ferran Valdez <>
Submitted on : Wednesday, July 4, 2007 - 2:44:07 PM
Last modification on : Thursday, January 7, 2021 - 4:22:12 PM
Long-term archiving on: : Thursday, April 8, 2010 - 10:32:56 PM


  • HAL Id : tel-00159918, version 1


Ferran Valdez. Feuilletages Homogènes et billards polygonaux. Mathématiques [math]. Université Rennes 1, 2007. Français. ⟨tel-00159918⟩



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