# American Institute of Mathematical Sciences

2018, 13: 199-219. doi: 10.3934/jmd.2018018

## Countable Markov partitions suitable for thermodynamic formalism

 1 Department of Mathematics, University of Maryland, College Park, MD 20742-4015, USA 2 Abdus Salam International Centre for Theoretical Physics, I - 34151 Trieste, Italy

To the memory of Roy Adler

Received  April 04, 2017 Revised  January 13, 2018 Published  December 2018

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 cross-sections 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 Hölder functions. The results are based on the methods developed by Sarig [26]-[28].

Citation: Michael Jakobson, Lucia D. Simonelli. Countable Markov partitions suitable for thermodynamic formalism. Journal of Modern Dynamics, 2018, 13: 199-219. doi: 10.3934/jmd.2018018
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