Given a convex billiard table, one defines the set ℳ swept by locally maximizing orbits for convex billiard. This is a remarkable closed invariant set which does not depend (under certain assumptions) on the choice of the generating function. I shall show how to get sharp estimates on the measure of this set, recovering as a corollary rigidity result for centrally symmetric convex billiards. Also I shall discuss rigidity of Mather β-function.
Based on joint works with Andrey E. Mironov, Sergei Tabachnikov and Daniel Tsodikovich
This video is part of the Institute for Advanced Study‘s Symplectic geometry seminar.
