|Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||Periodic Trajectories of Ellipsoidal Billiards in the 3-Dimensional Minkowski Space||Journal:||Asymptotic, Algebraic and Geometric Aspects of Integrable Systems||Series/Report no.:||Springer Proceedings in Mathematics & Statistics||Volume:||338||First page:||159||Last page:||174||Conference:||Asymptotic, Algebraic and Geometric Aspects of Integrable Systems Workshop, 2018; Sanya; China; 9 April 2018 through 13 April 2018||Issue Date:||24-Oct-2020||Rank:||M33||ISBN:||978-3-030-56999-0||ISSN:||2194-1009||DOI:||10.1007/978-3-030-57000-2_8||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.
|Keywords:||Ellipsoidal billiards | Hyper-elliptic curves | Pell’s equation | Periodic trajectories | Poncelet theorem | Pseudo-Euclidean spaces||Publisher:||Springer Link||Project:||Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems|
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