Closed geodesics and billiards on quadrics related to elliptic KdV solutions
Exactly Solvable and Integrable Systems
2009-02-26 v1 Dynamical Systems
Abstract
We consider algebraic geometrical properties of the integrable billiard on a quadric Q with elastic impacts along another quadric confocal to Q. These properties are in sharp contrast with those of the ellipsoidal Birkhoff billiards. Namely, generic complex invariant manifolds are not Abelian varieties, and the billiard map is no more algebraic. A Poncelet-like theorem for such system is known. We give explicit sufficient conditions both for closed geodesics and periodic billiard orbits on Q and discuss their relation with the elliptic KdV solutions and elliptic Calogero system
Keywords
Cite
@article{arxiv.nlin/0412034,
title = {Closed geodesics and billiards on quadrics related to elliptic KdV solutions},
author = {Simonetta Abenda and Yuri N. Fedorov},
journal= {arXiv preprint arXiv:nlin/0412034},
year = {2009}
}
Comments
23 pages, Latex, 1 figure Postscript