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January & February  2008, 22(1&2): 131-164. doi: 10.3934/dcds.2008.22.131

Thermodynamic formalism for random countable Markov shifts

Manfred Denker 1, , Yuri Kifer 2, and  Manuel Stadlbauer 1,

1. 

Institut für Mathematische Stochastik, Universität Göttingen, Maschmühlenweg 8-10, 37073 Göttingen, Germany, Germany
2. 

Einstein Institute of Mathematics, Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem, 91904, Israel

Received  July 2007 Revised  December 2007 Published  June 2008

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.
Keywords: variational principle, random countable shifts, thermodynamic formalism, random transformations..
Mathematics Subject Classification: Primary: 37D35; Secondary: 37H9.
Citation: Manfred Denker, Yuri Kifer, Manuel Stadlbauer. Thermodynamic formalism for random countable Markov shifts. Discrete & Continuous Dynamical Systems, 2008, 22 (1&2) : 131-164. doi: 10.3934/dcds.2008.22.131
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