Area spectral rigidity for axially symmetric symplectic billiard tables
Dynamical Systems
2026-05-11 v4
Abstract
We prove that any finitely smooth axially symmetric strictly convex domain, with everywhere positive curvature and sufficiently close to an ellipse is area spectrally rigid. This means that any area-isospectral family of domains in this class is necessarily equi-affine. We use techniques, adapted to symplectic billiards, inspired to the paper by J. De Simoi, V. Kaloshin and Q. Wei (2017).
Keywords
Cite
@article{arxiv.2410.12644,
title = {Area spectral rigidity for axially symmetric symplectic billiard tables},
author = {Luca Baracco and Olga Bernardi and Alessandra Nardi},
journal= {arXiv preprint arXiv:2410.12644},
year = {2026}
}