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Infinite genus surfaces and irrational polygonal billiards

2008/11/05 by Ferrán Valdez, Ferran Valdez, Valdez, Ferran
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 #math.DS

paper · pdf · doi:10.48550/arxiv.0811.0728

15 pages, 18 figures

openalex publication_date 2008/11/05 · arxiv created 2009/05/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the natural invariant surface associated with the billiard game on an irrational polygonal table is homeomorphic to the Loch Ness monster, that is, the only orientable infinite genus topological real surface with exactly one end.

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