Symbolic Dynamics and Markov Partitions for the Stadium Billiard

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.