Weighted thermodynamic formalism on subshifts and applications

Julien Barral and De-Jun Feng
Source: Asian J. Math. Volume 16, Number 2 (2012), 319-352.

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.

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