2013/12/01 by Jingyu Chen, Luke Mohr, Hong-Kun Zhang +1 · 1 citation
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · doi:10.1063/1.4850815
openalex publication_date 2013/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
In this paper, we study a two-parameter family of convex billiard tables, by taking the intersection of two round disks (with different radii) in the plane. These tables give a generalization of the one-parameter family of lemon-shaped billiards. Initially, there is only one ergodic table among all lemon tables. In our generalized family, we observe numerically the prevalence of ergodicity among the some perturbations of that table. Moreover, numerical estimates of the mixing rate of the billiard dynamics on some ergodic tables are also provided.