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Dimension Spectra of Hyperbolic Flows

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Abstract

For flows with a conformal hyperbolic set, we establish a conditional variational principle for the dimension spectra of Hölder continuous functions. We consider simultaneously Birkhoff averages into the future and into the past. We emphasize that the description of the spectra is not a consequence of the existing results for Birkhoff averages into the future (or into the past). The main difficulty is that even though the local product structure is bi-Lipschitz, the level sets of the Birkhoff averages are never compact. Our proof is based on the use of Markov systems and is inspired in earlier arguments in the case of discrete time.

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Authors and Affiliations

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

    Luis Barreira

  2. Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2829-516, Monte da Caparica, Portugal

    Paulo Doutor

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  1. Luis Barreira
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  2. Paulo Doutor
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Correspondence to Luis Barreira.

Additional information

L. Barreira was partially supported by FCT through CAMGSD, Lisbon.

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Barreira, L., Doutor, P. Dimension Spectra of Hyperbolic Flows. J Stat Phys 136, 505–525 (2009). https://doi.org/10.1007/s10955-009-9790-5

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  • DOI: https://doi.org/10.1007/s10955-009-9790-5

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