Zero Temperature Limits of Gibbs States for Almost-Additive Potentials

被引：0
作者：
Godofredo Iommi
Yuki Yayama
机构：
[1] Pontificia Universidad Católica de Chile (PUC),Facultad de Matemáticas
[2] Universidad del Bío-Bío,Departamento de Ciencias Básicas
来源：
Journal of Statistical Physics | 2014年 / 155卷
关键词：
Thermodynamic formalism; Ergodic optimisation; Gibbs measures; Almost-additive sequences; 37D35; 37D25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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 states 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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页码：23 / 46
页数：23
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共 70 条
  • [31] Fernández R(2005)A dynamical proof for the convergence of Gibbs measures at temperature zero Nonlinearity 18 2847-2880
  • [32] Sokal A(2001)Gibbs states on the symbolic space over an infinite alphabet Israel J. Math. 125 93-130
  • [33] Falconer KJ(2013)Sets for sequences of matrices and applications to the study of joint spectral radii Proc. London Math. Soc. 107 121-150
  • [34] Feng DJ(2006)The thermodynamic formalism for almost-additive sequences Discrete Contin. Dyn. Syst. 16 435-454
  • [35] Feng DJ(1990)Zeta functions and the periodic orbit structure of hyperbolic dynamics Asterisque 187–188 1-268
  • [36] Gripenberg G(1996)The joint spectral radius and invariant sets of linear operators Fundam. Prikl. Mat. 2 205-231
  • [37] Hare KG(1960)A note on the joint spectral radius Indag. Math. 22 379-381
  • [38] Morris I(1999)Thermodynamic formalism for countable Markov shifts Ergodic Theory Dynam. Systems 19 1565-1593
  • [39] Sidorov N(2003)Existence of Gibbs measures for countable Markov shifts Proc. Am. Math. Soc. 131 1751-1758
  • [40] Theys J(1998)On growth rates of subadditive functions for semiflows J. Differ. Equ. 148 334-350
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