On elliptical billiards in the Lobachevsky space and associated geodesic hierarchies

JOURNAL OF GEOMETRY AND PHYSICS

卷:47

Article

Dragovic, V ; Jovanovic, B ; Radnovic, M

关键词: integrable billiards;    Poncelet's theorem;    Cayley's condition;    spectral curve;    geodesic hierarchy;    separable perturbation;   

DOI  :  10.1016/S0393-0440(02)00219-X

来源: Elsevier

【 摘 要 】

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. (C) 2002 Elsevier Science B.V. All rights reserved.

【 授权许可】

Free