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arXiv · 1407.0555

Geodesic and billiard flows on quadrics in pseudo-Euclidean spaces: L-A pairs and Chasles theorem

Bozidar Jovanovic·Vladimir Jovanovic
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Abstract

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.

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Bozidar Jovanovic, Vladimir Jovanovic. 2014-09-04. Geodesic and billiard flows on quadrics in pseudo-Euclidean spaces: L-A pairs and Chasles theorem. https://arxiv.org/abs/1407.0555

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