Multifractal analysis of conformal axiom A flows

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Abstract

We develop the multifractal analysis of conformal axiom A flows. This includes the study of the Hausdorff dimension of basic sets of the flow, the description of the dimension spectra for pointwise dimension and for Lyapunov exponents and the multifractal decomposition associated with these spectra. The main tool of study is the thermodynamic formalism for hyperbolic flows by Bowen and Ruelle. Examples include suspensions over axiom A conformal diffeomorphisms, Anosov flows, and in particular, geodesic flows on compact smooth surfaces of negative curvature.

Original languageEnglish (US)
Pages (from-to)277-312
Number of pages36
JournalCommunications In Mathematical Physics
Volume216
Issue number2
DOIs
Publication statusPublished - Feb 1 2001

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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