On Elliptical Billiards in the Lobachevsky Space and associated Geodesic Hierarchies
Mathematical Physics
2009-11-07 v1 Dynamical Systems
math.MP
Abstract
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
Cite
@article{arxiv.math-ph/0210019,
title = {On Elliptical Billiards in the Lobachevsky Space and associated Geodesic Hierarchies},
author = {Vladimir Dragovic and Bozidar Jovanovic and Milena Radnovic},
journal= {arXiv preprint arXiv:math-ph/0210019},
year = {2009}
}
Comments
14 pages, to appear in Journal of Geometry and Physics