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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series A Année : 2018

Uniform hyperbolicity in nonflat billiards

Mickaël Kourganoff

Résumé

Uniform hyperbolicity is a strong chaotic property which holds, in particular, for Sinai billiards. In this paper, we consider the case of a nonflat billiard, that is, a Riemannian surface with boundary. Each trajectory follows the geodesic flow in the interior of the billiard, and bounces when it meets the boundary. We give a sufficient condition for a nonflat billiard to be uniformly hyperbolic. As a particular case, we obtain a new criterion to show that a closed surface has an Anosov geodesic flow.

Dates et versions

hal-01991263 , version 1 (23-01-2019)

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Mickaël Kourganoff. Uniform hyperbolicity in nonflat billiards. Discrete and Continuous Dynamical Systems - Series A, 2018, 38 (3), pp.1145-1160. ⟨10.3934/dcds.2018048⟩. ⟨hal-01991263⟩
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