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arXiv · 2008.06158

Pseudo-Euclidean Billiards within Confocal Curves on the Hyperboloid of One Sheet

Sean Gasiorek·Milena Radnovic
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Abstract

We consider a billiard problem for compact domains bounded by confocal conics on a hyperboloid of one sheet in the Minkowski space. We show that there are two types of confocal families in such setting. Using an algebro-geometric integration technique, we prove that the billiard within generalized ellipses of each type is integrable in the sense of Liouville. Further, we prove a generalization of the Poncelet theorem and derive Cayley-type conditions for periodic trajectories and explore geometric consequences.

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Sean Gasiorek, Milena Radnovic. 2020-08-14. Pseudo-Euclidean Billiards within Confocal Curves on the Hyperboloid of One Sheet. https://doi.org/10.1016/j.geomphys.2020.104032

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