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Topology of Integrable Billiard in an Ellipse in the Minkowski Plane with the Hooke Potential

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Abstract

The integrability of billiards bounded by arcs of confocal quadrics in the Minkowski plane in a field with the Hooke potential is obtained. The case of this type of a billiard in an ellipse is studied in detail. In addition to that, the topology of Liouville foliations arising in this problem is studied and Fomenko invariants are constructed.

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ACKNOWLEDGMENTS

The authors thank Academician A.T. Fomenko for problem formulation, constructive discussions, and valuable remarks given in the course of this study.

Funding

The work is carried out at the Lomonosov Moscow State University and is supported by the Russian Science Foundation, project no. 20-71-00155.

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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. V. Vedyushkina & A. I. Skvortsov

Authors
  1. V. V. Vedyushkina
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  2. A. I. Skvortsov
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Corresponding authors

Correspondence to V. V. Vedyushkina or A. I. Skvortsov.

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The authors declare that they have no conflicts of interest.

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Translated by E. Oborin

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Vedyushkina, V.V., Skvortsov, A.I. Topology of Integrable Billiard in an Ellipse in the Minkowski Plane with the Hooke Potential. Moscow Univ. Math. Bull. 77, 7–19 (2022). https://doi.org/10.3103/S0027132222010065

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