Elliptic non-degeneracy and spectral rigidity of classical billiards

2024/01/29 by Georgi Popov, Popov, Georgi, Peter Topalov +1
Mathematics · Physics and Astronomy · #35P20 #37J12 #37J35 #37J70 #53D25 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2401.16510

openalex publication_date 2024/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we show that the billiard ball map of the Liouville billiard tables of classical type on the ellipsoid is non-degenerate at the elliptic fixed point. As a corollary we obtain a spectral rigidity result.

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