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Pressure and equilibrium states for countable state markov shifts

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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.

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Correspondence to Doris Fiebig.

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Fiebig, D., Fiebig, UR. & Yuri, M. Pressure and equilibrium states for countable state markov shifts. Isr. J. Math. 131, 221–257 (2002). https://doi.org/10.1007/BF02785859

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  • DOI: https://doi.org/10.1007/BF02785859

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