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Multifractal analysis for countable Markov shifts

Published online by Cambridge University Press:  15 September 2005

GODOFREDO IOMMI
GODOFREDO IOMMI
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1949-001 Lisboa, Portugal (e-mail: [email protected])
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Abstract

We study the multifractal analysis of the pointwise dimension for equilibrium measures on countable Markov shifts. The main difficulty is that the space is not compact. In order to overcome this, we use an approximation argument based on the theory of convergence of Fenchel pairs developed by Wijsman. The results of Pesin and Weiss on multifractal analysis for compact spaces are used as well. We also prove a Bowen formula for countable Markov shifts. It turns out that, in this setting, this formula provides the Hausdorff dimension of the set of recurrent points.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 6 , December 2005 , pp. 1881 - 1907
Copyright
2005 Cambridge University Press

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