A few remarks on periodic orbits for planar billiard tables

2006/12/01 by Eugene Gutkin, Eugène Gutkin, Gutkin, Eugene
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.AP #math.DS

paper · pdf · doi:10.48550/arxiv.math/0612039

24 pages, 6 figures

arxiv created 2006/12/01 · openalex publication_date 2006/12/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I announce a solution of the conjecture about the measure of periodic points for planar billiard tables. The theorem says that if \Om⊂\R² is a compact domain with piecewise C³ boundary, then the set of periodic orbits for the billiard in \Om has measure zero. Here I outline a proof. A complete version will appear elsewhere.

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