Weighted thermodynamic formalism on subshifts and applications

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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Published 6 April 2012