Topology of billiard problems, II

2000/06/12 by Michael Färber, Michael Farber, Farber, Michael
Computer Science · Mathematics · Physics and Astronomy · #3Dxx #58Exx #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Topological and Geometric Data Analysis #math.AT #math.DG #msc:3Dxx #msc:58Exx

paper · pdf · doi:10.48550/arxiv.math/0006085

31 pages, 3 figures

arxiv created 2000/06/12 · openalex publication_date 2000/06/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give topological lower bounds on the number of periodic and closed trajectories in strictly convex smooth billiards. We use variational reduction admitting a finite group of symmetries and apply topological approach based on equivariant Morse and Lusternik - Schnirelman theories. The paper continues results published in math.DG/9911226 and math.DG/0006049

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