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arXiv · 1309.7924

Zero temperature limits of Gibbs states for almost-additive potentials

Godofredo Iommi·Yuki Yayama
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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.

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Godofredo Iommi, Yuki Yayama. 2013-10-24. Zero temperature limits of Gibbs states for almost-additive potentials. https://doi.org/10.1007/s10955-014-0943-9

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