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.Comment: 13 pages, 1 figur