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Algorithmic Construction of Two-Dimensional Singular Fibers of Atoms of Billiards in Non-Convex Domains

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Abstract

Planar billiards in nonconvex areas bounded by segments of confocal quadrics are studied. The topology of 2-dimensional fibers of Fomenko’s atoms is studied and a constructing algorithm is presented.

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ACKNOWLEDGMENTS

The author thanks A. T. Fomenko for problem formulation and attention to this work and V. V. Vedyushkina for multiple valuable discussions.

Funding

The study is supported by the Program of the President of the Russian Federation ‘‘Leading Scientific Schools of the Russian Federation’’ (grant no. NSh–6399.2018.1, agreement no. 075–02–2018–867).

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Authors and Affiliations

  1. Chair of Differential Geometry and Applications, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    V. A. Moskvin

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  1. V. A. Moskvin
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Correspondence to V. A. Moskvin.

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Translated by E. Oborin

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Moskvin, V.A. Algorithmic Construction of Two-Dimensional Singular Fibers of Atoms of Billiards in Non-Convex Domains. Moscow Univ. Math. Bull. 75, 91–101 (2020). https://doi.org/10.3103/S0027132220030043

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  • DOI: https://doi.org/10.3103/S0027132220030043

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