Break-up of resonant invariant circles in perturbations of the geodesic circular billiard on surfaces of constant curvature

2022/09/04 by Luciano Coutinho dos Santos, Santos, Luciano Coutinho dos, Sônia Pinto-de-Carvalho +1 · 1 citation
Mathematics · Physics and Astronomy · #37C05 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2209.01609

openalex publication_date 2022/09/04 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

We study the non-persistence of horizontal invariant circles for geodesically convex perturbations of the geodesic circular billiard on surfaces of constant curvature and show that the result obtained by Ramírez-Ros for the planar case, remains true for billiards on surfaces with constant curvature.

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