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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  • [1] Barreira L(2006)Nonadditive thermodynamic formalism: equilibrium and Gibbs measures Discrete Contin. Dyn. Syst. 16 279-305
  • [2] Barreira L(2009)Almost additive multifractal analysis J. Math. Pures Appl. 92 1-17
  • [3] Doutor P(2006)Multifractal analysis for Lyapunov exponents on nonconformal repellers Comm. Math. Phys. 267 393-418
  • [4] Barreira L(2010)Weak KAM methods and ergodic optimal problems for countable Markov shifts Bull. Braz. Math. Soc. (N.S.) 41 321-338
  • [5] Gelfert K(2000)Le poisson n’a pas d’aretes Ann. Inst. H. Poincare Probab. Statist. 36 489-508
  • [6] Bissacot R(2002)Asymptotic height optimization for topical IFS, Tetris heaps, and the finiteness conjecture J. Amer. Math. Soc. 15 77-111
  • [7] Garibaldi E(1979)Hausdorff dimension of quasicircles Inst. Hautes studes Sci. Publ. Math. 50 11-25
  • [8] Bousch T(2003)Gibbs measures at temperature zero Nonlinearity 16 419-426
  • [9] Bousch T(2010)On the zero-temperature limit of Gibbs states Comm. Math. Phys. 297 265-281
  • [10] Mairesse J(2011)Zero-temperature limit of one-dimensional Gibbs states via renormalization: the case of locally constant potentials Ergodic Theory Dynam. Systems 31 1109-1161
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