Countable Markov partitions suitable for thermodynamic formalism

Michael Jakobson; Lucia D. Simonelli

doi:10.3934/jmd.2018018

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

This volume Previous Article Seifert manifolds admitting partially hyperbolic diffeomorphisms Next Article Continuity of Lyapunov exponents for cocycles with invariant holonomies

Countable Markov partitions suitable for thermodynamic formalism

Michael Jakobson^1, and
Lucia D. Simonelli^2,

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 03, 2017

Revised: January 12, 2018

Published: December 2018

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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].

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

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