Article

Communications in Mathematical Physics

, Volume 78, Issue 2, pp 247-280

First online:

Markov Partitions for dispersed billiards

  • L. A. BunimovichAffiliated withL. D. Landau Institute for Theoretical Physics, Academy of Sciences
  • , Ya. G. SinaiAffiliated withL. D. Landau Institute for Theoretical Physics, Academy of Sciences

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Abstract

Markov Partitions for some classes of billiards in two-dimensional domains on ℝ2 or two-dimensional torus are constructed. Using these partitions we represent the microcanonical distribution of the corresponding dynamical system in the form of a limit Gibbs state and investigate the character of its approximations by finite Markov chains.