Thermodynamic formalism for random countable Markov shifts

Manfred Denker; Yuri Kifer; Manuel Stadlbauer

doi:10.3934/dcds.2008.22.131

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2008, Volume 22, Issue 1&2: 131-164. Doi: 10.3934/dcds.2008.22.131

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Thermodynamic formalism for random countable Markov shifts

1.
Institut für Mathematische Stochastik, Universität Göttingen, Maschmühlenweg 8-10, 37073 Göttingen
2.
Einstein Institute of Mathematics, Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem, 91904

Received: June 30, 2007

Revised: November 30, 2007

Published: February 2008

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Abstract

We introduce a relative Gurevich pressure for random countable topologically mixing Markov shifts. It is shown that the relative variational principle holds for this notion of pressure. We also prove a relative Ruelle-Perron-Frobenius theorem which enables us to construct a wealth of invariant Gibbs measures for locally fiber Hölder continuous functions. This is accomplished via a new construction of an equivariant family of fiber measures using Crauel's relative Prohorov theorem. Some properties of the Gibbs measures are discussed as well.

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Mathematics Subject Classification: Primary: 37D35; Secondary: 37H99.

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