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June 2012 Weighted thermodynamic formalism on subshifts and applications
Julien Barral, De-Jun Feng
Asian J. Math. 16(2): 319-352 (June 2012).

Abstract

We examine the interplay between the thermodynamic formalism and the multifractal formalism on the so-called self-affine symbolic spaces, under the specification property assumption. We investigate the properties of a weighted variational principle to derive a new result concerning the approximation of any invariant probability measure $\mu$ by sequences of weighted equilibrium states whose weighted entropies converge to the weighted entropy of $\mu$. This is a key property in the estimation of the Hausdorff dimension of sets of generic points, and then in the multifractal analysis of non homogeneous Birkhoff averages.

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Julien Barral. De-Jun Feng. "Weighted thermodynamic formalism on subshifts and applications." Asian J. Math. 16 (2) 319 - 352, June 2012.

Information

Published: June 2012
First available in Project Euclid: 9 April 2012

zbMATH: 1261.37016
MathSciNet: MR2916367

Subjects:
Primary: 37D35
Secondary: 28A78 , 37A35 , 37B10

Keywords: affine invariant sets , equilibrium states , Hausdorff dimension , Multifractal analysis , symbolic dynamics , Thermodynamic formalism

Rights: Copyright © 2012 International Press of Boston

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Vol.16 • No. 2 • June 2012
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