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
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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