Uniform hyperbolicity in nonflat billiards

Abstract

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 manifold 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.

19 pages

References in corpus (2)

• Exponential Decay of Correlations for Finite Horizon Sinai Billiard Flows
• Embedded surfaces with Anosov geodesic flows, approximating spherical billiards

Cited by in corpus (3)

• Travelling Times in Scattering by Obstacles in Curved Space
• A new proof of the existence of embedded surfaces with Anosov geodesic flow
• The Morse index theorem for mechanical systems with reflections