The billiard inside an ellipse deformed by the curvature flow
Dynamical Systems
2023-09-19 v1
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.
Keywords
Cite
@article{arxiv.1511.01355,
title = {The billiard inside an ellipse deformed by the curvature flow},
author = {Josue Damasceno and Mario J. Dias Carneiro and Rafael Ramirez-Ros},
journal= {arXiv preprint arXiv:1511.01355},
year = {2023}
}
Comments
13 pages, 1 figure