Symbolic Dynamics and Markov Partitions for the Stadium Billiard
chao-dyn
2016-08-31 v1 Chaotic Dynamics
Abstract
We investigate the Bunimovich stadium dynamics and find that in the limit of infinitely long stadium the symbolic dynamics is a subshift of finite type. For a stadium of finite length the Markov partitions are infinite, but the inadmissible symbol sequences can be determined exactly by means of the appropriate pruning front. We outline a construction of a sequence of finite Markov graph approximations by means of approximate pruning fronts with finite numbers of steps.
Keywords
Cite
@article{arxiv.chao-dyn/9502005,
title = {Symbolic Dynamics and Markov Partitions for the Stadium Billiard},
author = {Kai T. Hansen and Predrag Cvitanovic},
journal= {arXiv preprint arXiv:chao-dyn/9502005},
year = {2016}
}
Comments
31 pages PostScript uuencoded with figures