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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.

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Authors and Affiliations

  1. Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA.¶E-mail: pesin@math.psu.edu; sadovski@math.psu.edu, , , , , , US

    Ya. B. Pesin & V. Sadovskaya

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  1. Ya. B. Pesin
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  2. V. Sadovskaya
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Received: 18 November 1999 / Accepted: 24 July 2000

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Pesin, Y., Sadovskaya, V. Multifractal Analysis of Conformal Axiom A Flows. Commun. Math. Phys. 216, 277–312 (2001). https://doi.org/10.1007/s002200000329

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  • DOI: https://doi.org/10.1007/s002200000329

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