Symbolic Dynamics and Markov Partitions for the Stadium Billiard

Kai T. Hansen; Predrag Cvitanovic

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arXiv · chao-dyn/9502005

Symbolic Dynamics and Markov Partitions for the Stadium Billiard

Kai T. Hansen·Predrag Cvitanovic

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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.

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Kai T. Hansen, Predrag Cvitanovic. 1995-02-06. Symbolic Dynamics and Markov Partitions for the Stadium Billiard. https://arxiv.org/abs/chao-dyn/9502005

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