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arXiv · 1511.01355

The billiard inside an ellipse deformed by the curvature flow

Josue Damasceno·Mario J. Dias Carneiro·Rafael Ramirez-Ros
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Abstract

The billiard dynamics inside an ellipse is integrable. It has zero topological entropy, four separatrices in the phase space, and a continuous family of convex caustics: the confocal ellipses. We prove that the curvature flow destroys the integrability, increases the topological entropy, splits the separatrices in a transverse way, and breaks all resonant convex caustics.

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Josue Damasceno, Mario J. Dias Carneiro, Rafael Ramirez-Ros. 2015-11-04. The billiard inside an ellipse deformed by the curvature flow. https://arxiv.org/abs/1511.01355

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