Totally integrable symplectic billiards are ellipses
Dynamical Systems
2026-05-11 v1
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.
Keywords
Cite
@article{arxiv.2305.19701,
title = {Totally integrable symplectic billiards are ellipses},
author = {Luca Baracco and Olga Bernardi},
journal= {arXiv preprint arXiv:2305.19701},
year = {2026}
}
Comments
11 pages, 1 figure