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Israel Journal of Mathematics

, Volume 131, Issue 1, pp 221–257 | Cite as

Pressure and equilibrium states for countable state markov shifts

  • Doris Fiebig
  • Ulf-Rainer Fiebig
  • Michiko Yuri
Article

Abstract

We give a general definition of the topological pressureP top (f, S) for continuous real valued functionsf: X→ℝ on transitive countable state Markov shifts (X, S). A variational principle holds for functions satisfying a mild distortion property. We introduce a new notion of Z-recurrent functions. Given any such functionf, we show a general method how to obtain tight sequences of invariant probability measures supported on periodic points such that a weak accumulation pointμ is an equilibrium state forf if and only if εf <∞. We discuss some conditions that ensure this integrability. As an application we obtain the Gauss measure as a weak limit of measures supported on periodic points.

Keywords

Variational Principle Periodic Point Gauss Measure Invariant Probability Measure Bernoulli Shift 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Hebrew University Magnes Press 2002

Authors and Affiliations

  1. 1.Institut für Mathematische StochastikUniversität GöttingenGöttingenGermany
  2. 2.Institut für Angewandte MathematikUniversität HeidelbergHeidelbergGermany
  3. 3.Department of Business AdministrationSapporo University NishiokaToyohira-ku, SapporoJapan

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