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Countable Markov partitions suitable for thermodynamic formalism

To the memory of Roy Adler

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  • 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].

    Mathematics Subject Classification: Primary: 37D35; Secondary: 37B10, 37C30, 37C70, 37D40, 37D45.

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