  For 2-d hyperbolic systems with singularities, statistical properties are
rather difficult to establish because of the fragmentation of the phase space
by singular curves. In this paper, we construct a Markov partition of the phase
space with countable states for a general class of hyperbolic systems with
singularities. Stochastic properties with respect to the SRB measure
immediately follow from our construction of the Markov partition, including the
decay rates of correlations and the central limit theorem. We further establish
the thermodynamic formalism for the family of geometric potentials, by using
the inducing scheme of hyperbolic type. All the results apply to Sinai
dispersing billiards, and their small perturbations due to external forces and
nonelastic reflections with kicks and slips.
