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Suspension Flows Over Countable Markov Shifts

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Abstract

We introduce the notion of topological pressure for suspension flows over countable Markov shifts, and we develop the associated thermodynamic formalism. In particular, we establish a variational principle for the topological pressure, and an approximation property in terms of the pressure on compact invariant sets. As an application we present a multifractal analysis for the entropy spectrum of Birkhoff averages for suspension flows over countable Markov shifts. The domain of the spectrum may be unbounded and the spectrum may not be analytic. We provide explicit examples where this happens. We also discuss the existence of full measures on the level sets of the multifractal decomposition.

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Authors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, 1049-001, Lisboa, Portugal

    Luis Barreira & Godofredo Iommi

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  1. Luis Barreira
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  2. Godofredo Iommi
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Correspondence to Luis Barreira.

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Barreira, L., Iommi, G. Suspension Flows Over Countable Markov Shifts. J Stat Phys 124, 207–230 (2006). https://doi.org/10.1007/s10955-006-9140-9

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  • DOI: https://doi.org/10.1007/s10955-006-9140-9

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