| Authors: | Dragović, Vladimir Radnović, Milena |
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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