English

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