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math-ph2002★ 20 cited
On Elliptical Billiards in the Lobachevsky Space and associated Geodesic Hierarchies
Vladimir Dragovic, Bozidar Jovanovic, Milena Radnovic
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 f…
math-ph2002★ 2 cited
On the integrability of geodesic flows of submersion metrics
Bozidar Jovanovic
Suppose we are given a compact Riemannian manifold (Q,g)with completely integrable geodesic flow. Let G be a compact connected Lie group acting freely on Q by isometries. The natur…