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arXiv · 1006.3104

Chaos and stability in a two-parameter family of convex billiard tables

Péter Bálint·Miklós Halász·Jorge Hernández-Tahuilán·David P. Sanders
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Abstract

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.

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Péter Bálint, Miklós Halász, Jorge Hernández-Tahuilán, David P. Sanders. 2010-06-15. Chaos and stability in a two-parameter family of convex billiard tables. https://doi.org/10.1088/0951-7715%2F24%2F5%2F006

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