Length Spectrum Rigidity for piecewise analytic Bunimovich Billiards

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