Chaos and stability in a two-parameter family of convex billiard tables
We study, by numerical simulations and semi-rigorous arguments, a two-parameter family of convex, two-dimensional billiard tables, generalizing the one-parameter class of oval billiards of Benettin--Strelcyn [Phys. Rev. A 17, 773 (1978)]. We observe interesting dynamical phenomena when the billiard...
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| creator | Bálint, Péter Halász, Miklós Hernández-Tahuilán, Jorge Sanders, David P |
| description | We study, by numerical simulations and semi-rigorous arguments, a two-parameter family of convex, two-dimensional billiard tables, generalizing the one-parameter class of oval billiards of Benettin--Strelcyn [Phys. Rev. A 17, 773 (1978)]. We observe interesting dynamical phenomena when the billiard tables are continuously deformed from the integrable circular billiard to different versions of completely-chaotic stadia. In particular, we conjecture that a new class of ergodic billiard tables is obtained in certain regions of the two-dimensional parameter space, when the billiards are close to skewed stadia. We provide heuristic arguments supporting this conjecture, and give numerical confirmation using the powerful method of Lyapunov-weighted dynamics. |
| doi_str_mv | 10.48550/arxiv.1006.3104 |
| format | Article |
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| source | Freely Accessible Journals; arXiv.org |
| subjects | Billiards Computer simulation Deformation Market strategy Mathematics - Dynamical Systems Parameters Physics - Chaotic Dynamics |
| title | Chaos and stability in a two-parameter family of convex billiard tables |
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