Multifractal analysis of conformal axiom A flows

Ya B. Pesin; V. Sadovskaya

doi:10.1007/s002200000329

Multifractal analysis of conformal axiom A flows

Ya B. Pesin, V. Sadovskaya

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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 language	English (US)
Pages (from-to)	277-312
Number of pages	36
Journal	Communications In Mathematical Physics
Volume	216
Issue number	2
DOIs	https://doi.org/10.1007/s002200000329
State	Published - Feb 2001

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s002200000329

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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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Multifractal analysis of conformal axiom A flows

Abstract

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