Length Spectrum Rigidity for piecewise analytic Bunimovich Billiards
Dynamical Systems
2022-07-26 v4
Abstract
In the paper, we establish Squash Rigidity Theorem - the dynamical spectral rigidity for piecewise analytic Bunimovich squash-type stadia. We also establish Stadium Rigidity Theorem - the dynamical spectral rigidity for piecewise analytic Bunimovich stadia whose flat boundaries are a priori fixed. In addition, for smooth Bunimovich squash-type stadia we compute the Lyapunov exponents along the maximal period two orbit, as well as the value of the Peierls' Barrier function from the maximal marked length spectrum associated to the rotation number .
Cite
@article{arxiv.1902.07330,
title = {Length Spectrum Rigidity for piecewise analytic Bunimovich Billiards},
author = {Jianyu Chen and Vadim Kaloshin and Hong-Kun Zhang},
journal= {arXiv preprint arXiv:1902.07330},
year = {2022}
}