Hopf rigidity for convex billiards on the hemisphere and hyperbolic plane

2012/05/17 by Michael, Bialy · 4 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DG #math.DS #nlin.SI

paper · pdf · doi:10.48550/arxiv.1205.3873

12 p, revised version, corrected typos

openalex publication_date 2012/05/17 · arxiv created 2012/09/25 · arxiv updated 2012/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper deals with Hopf type rigidity for convex billiards on surfaces of constant curvature. We prove that the only convex billiard without conjugate points on the Hyperbolic plane or on the Hemisphere is circular billiard.

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• Lyapunov exponents and rigidity in random billiards and standard maps
• Integrable Billiards and Related Topics
• On complex algebraic caustics in planar and projective billiards
• Optical Billiards

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