Dynamical Spectral rigidity among $\mathbb Z_2$-symmetric strictly convex domains close to a circle
Dynamical Systems
2017-03-20 v3 Spectral Theory
Abstract
We show that any sufficiently (finitely) smooth -symmetric strictly convex domain sufficiently close to a circle is dynamically spectrally rigid, i.e. all deformations among domains in the same class which preserve the length of all periodic orbits of the associated billiard flow must necessarily be isometric deformations. This gives a partial answer to a question of P. Sarnak.
Keywords
Cite
@article{arxiv.1606.00230,
title = {Dynamical Spectral rigidity among $\mathbb Z_2$-symmetric strictly convex domains close to a circle},
author = {Jacopo De Simoi and Vadim Kaloshin and Qiaoling Wei and with an appendix joint with Hamid Hezari},
journal= {arXiv preprint arXiv:1606.00230},
year = {2017}
}