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Ergodic Optimization for Renewal Type Shifts

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Abstract.

We consider a class of countable Markov shifts \({\cal R}\) and a locally Hölder potential φ. We prove that the existence of φ-optimal measures is closely related to the behaviour of the pressure function t → P(tφ). Using a Theorem by Sarig it is possible to prove that there exists a critical value t c ∈ (0, ∞] such that for t < t c the pressure is analytic and for t > t c is linear. We prove that if t c is finite, then there are no φ-optimal measures, and if it is infinite, then φ-optimal measures do exist.

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Authors and Affiliations

  1. Instituto Superior Técnico, Lisboa, Portugal

    Godofredo Iommi

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  1. Godofredo Iommi
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Additional information

The author was partially supported by FCT/POCTI/FEDER and the grant SFRH/BPD/21927/2005.

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Iommi, G. Ergodic Optimization for Renewal Type Shifts. Mh Math 150, 91–95 (2007). https://doi.org/10.1007/s00605-005-0389-x

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  • DOI: https://doi.org/10.1007/s00605-005-0389-x

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