English

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 2n4n+1\frac{2n}{4n+1}.

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}
}
R2 v1 2026-06-23T07:45:30.796Z