Zero temperature limits of Gibbs states for almost-additive potentials

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.

Changes in Sections 4 and 5 are included in this version

References in corpus (1)

• Ergodic optimization, zero temperature limits and the max-plus algebra

Cited by in corpus (3)

• Ergodic optimization in dynamical systems
• Additive, almost additive and asymptotically additive potential sequences are equivalent
• Combined mean-field and semiclassical limits of large fermionic systems