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For 2-d hyperbolic systems with singularities, statistical properties arerather difficult to establish because of the fragmentation of the phase spaceby singular curves. In this paper, we construct a Markov partition of the phasespace with countable states for a general class of hyperbolic systems withsingularities. Stochastic properties with respect to the SRB measureimmediately follow from our construction of the Markov partition, including thedecay rates of correlations and the central limit theorem. We further establishthe thermodynamic formalism for the family of geometric potentials, by usingthe inducing scheme of hyperbolic type. All the results apply to Sinaidispersing billiards, and their small perturbations due to external forces andnonelastic reflections with kicks and slips.

Markov partition and Thermodynamic Formalism for Hyperbolic Systems with Singularities