  We study hyperbolic attractors of some dynamical systems with apriori given
countable Markov partitions. Assuming that contraction is stronger than
expansion we construct new Markov rectangles such that their crossections by
unstable manifolds are Cantor sets of positive Lebesgue measure. Using new
Markov partitions we develop thermodynamical formalism and prove exponential
decay of correlations and related properties for certain H\"older functions.
The results are based on the methods developed by Sarig.
