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Orbital Invariants of Flat Billiards Bounded by Arcs of Confocal Quadrics and Containing Focuses

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Abstract

Rotation functions for flat billiards bounded by arcs of confocal quadrics and containing focuses are calculated. The orbital Bolsinov–Fomenko invariants of these dynamical systems are also calculated.

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REFERENCES

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ACKNOWLEDGMENTS

The authors thanks A.T. Fomenko for multiple valuable comments and attention to this work.

Funding

The study is supported by the Russian Science Foundation, project no. 17-11-01303.

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Authors and Affiliations

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

    V. V. Vedyushkina

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  1. V. V. Vedyushkina
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Correspondence to V. V. Vedyushkina.

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Translated by E. Oborin

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Vedyushkina, V.V. Orbital Invariants of Flat Billiards Bounded by Arcs of Confocal Quadrics and Containing Focuses. Moscow Univ. Math. Bull. 76, 177–180 (2021). https://doi.org/10.3103/S0027132221040070

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  • DOI: https://doi.org/10.3103/S0027132221040070

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