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Periodic Trajectories of Ellipsoidal Billiards in the 3-Dimensional Minkowski Space

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Asymptotic, Algebraic and Geometric Aspects of Integrable Systems

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 338))

Abstract

In this paper, we give detailed analysis and description of periodic trajectories of the billiard system within an ellipsoid in the 3-dimensional Minkowski space, taking into account all possibilities for the caustics. The conditions for periodicity are derived in algebro-geometric, analytic, and polynomial form.

Dedicated to Professor Nalini Joshi on the occasion of her anniversary.

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Acknowledgements

The research of V. D. and M. R. was supported by the Discovery Project #DP190101838 Billiards within confocal quadrics and beyond from the Australian Research Council and Project #174020 Geometry and Topology of Manifolds, Classical Mechanics and Integrable Systems of the Serbian Ministry of Education, Technological Development and Science. The authors are grateful to the referee for careful reading and very useful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematical Sciences, The University of Texas at Dallas, Richardson, USA

    Vladimir Dragović

  2. The University of Sydney, School of Mathematics and Statistics, Sydney, Australia

    Milena Radnović

  3. Mathematical Institute SANU, Belgrade, Serbia

    Vladimir Dragović & Milena Radnović

Authors
  1. Vladimir Dragović
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  2. Milena Radnović
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Corresponding author

Correspondence to Milena Radnović .

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Editors and Affiliations

  1. School of Mathematics, University of Leeds, Leeds, UK

    Frank Nijhoff

  2. College of Science and Engineering, Flinders at Tonsley, Adelaide, SA, Australia

    Yang Shi

  3. Department of Mathematics, Shanghai University, Shanghai, China

    Da-jun Zhang

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Dragović, V., Radnović, M. (2020). Periodic Trajectories of Ellipsoidal Billiards in the 3-Dimensional Minkowski Space. In: Nijhoff, F., Shi, Y., Zhang, Dj. (eds) Asymptotic, Algebraic and Geometric Aspects of Integrable Systems. Springer Proceedings in Mathematics & Statistics, vol 338. Springer, Cham. https://doi.org/10.1007/978-3-030-57000-2_8

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