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arXiv · 2201.01362

Billiards in generic convex bodies have positive topological entropy

Mário Bessa·Gianluigi Del Magno·João Lopes Dias·José Pedro Gaivão·Maria Joana Torres
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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.

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Mário Bessa, Gianluigi Del Magno, João Lopes Dias, José Pedro Gaivão, Maria Joana Torres. 2022-01-04. Billiards in generic convex bodies have positive topological entropy. https://arxiv.org/abs/2201.01362

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