The billiard inside an ellipse deformed by the curvature flow

TL;DR

This paper investigates how the curvature flow affects the integrable billiard dynamics inside an ellipse, showing that it destroys integrability, increases entropy, and breaks caustics.

Contribution

It provides a rigorous analysis of the effects of curvature flow on elliptical billiards, revealing the transition from integrability to chaos.

Findings

Curvature flow destroys billiard integrability inside an ellipse.

Topological entropy increases under curvature flow.

All resonant convex caustics are broken by the flow.

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.