Billiards in generic convex bodies have positive topological entropy

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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Bibliographic Details
Published in:arXiv.org 2024-02
Main Authors: Bessa, Mário, Gianluigi Del Magno, João Lopes Dias, José Pedro Gaivão, Torres, Maria Joana
Format: Article
Language:English
Subjects:
Billiards
Entropy
Orbits
Smooth boundaries
Topology
Online Access:Get full text
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Description
Summary: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.
ISSN:2331-8422