Asian Journal of Mathematics
Volume 16 (2012)
Weighted thermodynamic formalism on subshifts and applications
Pages: 319 – 352
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.
Thermodynamic formalism; equilibrium states; symbolic dynamics; affine invariant sets; multifractal analysis; Hausdorff dimension
2010 Mathematics Subject Classification
Primary 37D35. Secondary 28A78, 37A35, 37B10.