Asian Journal of Mathematics

Volume 16 (2012)

Number 2

Weighted thermodynamic formalism on subshifts and applications

Pages: 319 – 352

DOI: http://dx.doi.org/10.4310/AJM.2012.v16.n2.a8

Authors

Julien Barral

De-Jun Feng

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.

Keywords

Thermodynamic formalism; equilibrium states; symbolic dynamics; affine invariant sets; multifractal analysis; Hausdorff dimension

2010 Mathematics Subject Classification

Primary 37D35. Secondary 28A78, 37A35, 37B10.

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