Billiards in generic convex bodies have positive topological entropy

Abstract

We show that there exists a $C^2$ open dense set of convex bodies with smooth boundary whose billiard map exhibits a non-trivial hyperbolic basic set. As a consequence billiards in generic convex bodies have positive topological entropy and exponential growth of the number of periodic orbits.

33 pages

References in corpus (3)

• Realization of tangent perturbations in discrete and continuous time conservative systems
• Local perturbations of conservative $C^1$-diffeomorphisms
• Counting Periodic Trajectories of Finsler Billiards