1 research outputs found
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
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.Comment: 19 pages, 13 figures. Submitted for publication. Supplementary video
available at http://sistemas.fciencias.unam.mx/~dsanders