Authors: Dragović, Vladimir 
Jovanović, Božidar 
Radnović, Milena
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On elliptical billiards in the Lobachevsky space and associated geodesic hierarchies
Journal: Journal of Geometry and Physics
Volume: 47
Issue: 2-3
First page: 221
Last page: 234
Issue Date: 1-Jan-2003
Rank: M21
ISSN: 0393-0440
DOI: 10.1016/S0393-0440(02)00219-X
We derive Cayley's type conditions for periodical trajectories for the billiard within an ellipsoid in the Lobachevsky space. It appears that these new conditions are of the same form as those obtained before for the Euclidean case. We explain this coincidence by using theory of geodesically equivalent metrics and show that Lobachevsky and Euclidean elliptic billiards can be naturally considered as a part of a hierarchy of integrable elliptical billiards.
Keywords: Cayley's condition | Geodesic hierarchy | Integrable billiards | Poncelet's theorem | Separable perturbation | Spectral curve
Publisher: Elsevier
Project: Serbian Ministry of Science and Technology, Project 1643 - Geometry and Topology of Manifolds and Integrable Dynamical Systems
Geometry and Topology of Manifolds and Integrable Dynamical Systems 

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