Zero temperature limits of Gibbs states for almost-additive potentials
Dynamical Systems
2015-06-17 v4
Abstract
This paper is devoted to study ergodic optimisation problems for almost-additive sequences of functions (rather than a fixed potential) defined over countable Markov shifts (that is a non-compact space). Under certain assumptions we prove that any accumulation point of a family of Gibbs equilibrium measures is a maximising measure. Applications are given in the study of the joint spectral radius and to multifractal analysis of Lyapunov exponent of non-conformal maps.
Cite
@article{arxiv.1309.7924,
title = {Zero temperature limits of Gibbs states for almost-additive potentials},
author = {Godofredo Iommi and Yuki Yayama},
journal= {arXiv preprint arXiv:1309.7924},
year = {2015}
}
Comments
Changes in Sections 4 and 5 are included in this version