Dragović, Vladimir; Jovanović, Božidar Žarko; Radnović, Milena On elliptical billiards in the Lobachevsky space and associated geodesic hierarchies. (English) Zbl 1061.70010 J. Geom. Phys. 47, No. 2-3, 221-234 (2003). Summary: We derive Cayley’s type conditions for periodic trajectories for a billiard within an ellipsoid in the Lobachevsky space. It appears that these new conditions are of the same form as those obtained 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. Cited in 8 Documents MSC: 70H06 Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics 37N05 Dynamical systems in classical and celestial mechanics 37J10 Symplectic mappings, fixed points (dynamical systems) (MSC2010) 37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) 53D25 Geodesic flows in symplectic geometry and contact geometry Keywords:integrable billiards; Cayley condition; periodic trajectories PDFBibTeX XMLCite \textit{V. Dragović} et al., J. Geom. Phys. 47, No. 2--3, 221--234 (2003; Zbl 1061.70010) Full Text: DOI arXiv References: [1] V. Arnol’d, Mathematical Methods of Classical Mechanics, Springer, Berlin, 1978.; V. Arnol’d, Mathematical Methods of Classical Mechanics, Springer, Berlin, 1978. [2] S. Benenti, Orthogonal separable dynamical systems, in: Differential Geometry and its Applications (Opava, 1992), pp. 163-184, Math. 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