Authors: Jovanović, Božidar 
Jovanović, Vladimir
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Geodesic and Billiard Flows on Quadrics in Pseudo-Euclidean Spaces: L-A Pairs and Chasles Theorem
Journal: International Mathematics Research Notices
Volume: 2015
Issue: 15
First page: 6618
Last page: 6638
Issue Date: 1-Jan-2015
Rank: M21
ISSN: 1073-7928
DOI: 10.1093/imrn/rnu141
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.
Publisher: Oxford University Press

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