Thermodynamic formalism for random countable Markov shifts

Manfred Denker, Yuri Kifer, Manuel Stadlbauer

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)131-164
Number of pages34
JournalDiscrete and Continuous Dynamical Systems
Volume22
Issue number1-2
DOIs
StatePublished - 2008

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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