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


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.


Variational Principle Periodic Point Gauss Measure Invariant Probability Measure Bernoulli Shift 
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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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