Local rigidity for symplectic billiards
Dynamical Systems
2025-09-01 v2
Abstract
We show a local rigidity result for the integrability of symplectic billiards. We prove that any domain which is close to an ellipse, and for which the symplectic billiard map is rationally integrable must be an ellipse as well. This is in spirit of the result of Avila, De Simoi, and Kaloshin for Birkhoff billiards.
Keywords
Cite
@article{arxiv.2501.08849,
title = {Local rigidity for symplectic billiards},
author = {Daniel Tsodikovich},
journal= {arXiv preprint arXiv:2501.08849},
year = {2025}
}
Comments
27 pages, 2 figures. Minor revisions