Dimension spectrum of axiom a diffeomorphisms. I. The Bowen-Margulis measure |
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Authors: | Dominique Simpelaere |
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Affiliation: | (1) Laboratoire de Probabilités, Tour 56, Université Pierre et Marie Curie, Paris VI, 4 Place Jussieu, Paris Cedex 05, France |
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Abstract: | We compute the dimension spectrumf() of the singularity sets of the Bowen-Margulis measure defined on a two-dimensional compact manifold and invariant with respect to aC2 Axiom A diffeomorphism. It is proved thatf is the Legendre-Fenchel transform of a free energy function which is real analytic (linear in the degenerate case). The functionf is also real analytic on its definition domain (defined in one point in the degenerate case) and is related to the Hausdorff dimensions of Gibbs measures singular with respect to each other and whose supports are the singularity sets, and we decompose these sets. |
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Keywords: | Multifractal thermodynamic formalism Hausdorff dimension free energy function large deviations Gibbs measures |
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