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On Closed Geodesics on Ellipsoids
Vladimir Dragovic, Milena Radnovic
Closed geodesic lines on an ellipsoid in d-dimensional Euclidean space are considered. Explicit algebro-geometric condition for closedness of such a geodesic is given. The obtained…
Geometry of Integrable Billiards and Pencils of Quadrics
Vladimir Dragovic, Milena Radnovic
We study the deep interplay between geometry of quadrics in d-dimensional space and the dynamics of related integrable billiard systems. Various generalizations of Poncelet theorem…
Cayley-Type Conditions for Billiards within Quadrics in
Vladimir Dragovic, Milena Radnovic
The notions of reflection from outside, reflection from inside and signature of a billiard trajectory within a quadric are introduced. Cayley-type conditions for periodical traject…
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…