Billiards in generic convex bodies have positive topological entropy

2022/01/04 by Mário Bessa, Bessa, Mário, Gianluigi Del Magno +7 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2201.01362

openalex publication_date 2022/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that there exists a C² 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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