Geodesic and Billiard Flows on Quadrics in Pseudo-Euclidean Spaces: L-A Pairs and Chasles Theorem

Abstract

For permissions, please e-mail: journals.permissions@oup.com. In this article, we construct L-A representations of geodesic flows on quadrics and of billiard problems within ellipsoids in the pseudo-Euclidean spaces. A geometric interpretation of the integrability analogous to the classical Chasles theorem for symmetric ellipsoids is given. We also consider a generalization of the billiard within arbitrary quadric allowing virtual billiard reflections.