Multifractal analysis of the irregular set for almost-additive sequences via large deviations

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.

23 pages, to appear in Nonlinearity; small changes made according to comments from the referees

Cited by in corpus (6)

• On entropy production of repeated quantum measurements I. General theory
• Additive, almost additive and asymptotically additive potential sequences are equivalent
• Multifractal analysis for weak Gibbs measures: from large deviations to irregular sets
• Abundance of wild historic behavior
• Fluctuation Theorem and Thermodynamic Formalism
• Irregular sets for piecewise monotonic maps