Totally integrable symplectic billiards are ellipses

Abstract

In this paper we prove that a totally integrable strictly-convex symplectic billiard table, whose boundary has everywhere strictly positive curvature, must be an ellipse. The proof, inspired by the analogous result of Bialy for Birkhoff billiards, uses the affine equivariance of the symplectic billiard map.

11 pages, 1 figure

Cited by in corpus (2)

• Starting the study of outer length billiards
• Local rigidity for symplectic billiards