Multifractal analysis of the irregular set for almost-additive sequences via large deviations
Dynamical Systems
2015-09-30 v2
Abstract
In this paper we introduce a notion of free energy and large deviations rate function for asymptotically additive sequences of potentials via an approximation method by families of continuous potentials. We provide estimates for the topological pressure of the set of points whose non-additive sequences are far from the limit described through Kingman's sub-additive ergodic theorem and give some applications in the context of Lyapunov exponents for diffeomorphisms and cocycles, and Shannon-McMillan-Breiman theorem for Gibbs measures.
Cite
@article{arxiv.1410.2220,
title = {Multifractal analysis of the irregular set for almost-additive sequences via large deviations},
author = {Thiago Bomfim and Paulo Varandas},
journal= {arXiv preprint arXiv:1410.2220},
year = {2015}
}
Comments
23 pages, to appear in Nonlinearity; small changes made according to comments from the referees