Ergodicity of the generalized lemon billiards. (English) Zbl 1331.37006
Summary: 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.{
©2013 American Institute of Physics}
©2013 American Institute of Physics}
MSC:
| 37A25 | Ergodicity, mixing, rates of mixing |
| 37D50 | Hyperbolic systems with singularities (billiards, etc.) (MSC2010) |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 37D05 | Dynamical systems with hyperbolic orbits and sets |
| 37M05 | Simulation of dynamical systems |
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