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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