How smooth can convex chaotic billiard tables be?
Dynamical Systems
2018-06-11 v1
Abstract
We solve the longstanding problem of smoothing a stadium billiard. Besides our results demonstrate why there were no clear conjectures how much the stadium's boundary must be smoothened to destroy chaotic dynamics. To do that we needed to extend standard KAM theory to analyze stability of periodic orbits, because of the low smoothness of the system. In fact, the stadium has a boundary, and we show that smoothing results in appearance of elliptic periodic orbits.
Keywords
Cite
@article{arxiv.1806.02961,
title = {How smooth can convex chaotic billiard tables be?},
author = {Leonid Bunimovich and Alexander Grigo},
journal= {arXiv preprint arXiv:1806.02961},
year = {2018}
}