Uniqueness of the measure with full dimension on sofic affine-invariant subsets of the 2-torus

被引：11

作者：

Olivier, Eric ^{[1
]}

机构：

[1] Univ Aix Marseille 1, LATP, CNRS, UMR 6632, Marseille, France

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2010年 / 30卷

关键词：

COUNTABLE MARKOV SHIFTS; VARIATIONAL PRINCIPLE; EXPANDING MAPS; THERMODYNAMIC FORMALISM; MULTIFRACTAL FORMALISM; GIBBS MEASURES; EXCEPTIONAL PHENOMENA; HAUSDORFF DIMENSION; SYSTEMS; ENTROPY;

D O I：

10.1017/S0143385709000546

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the variational principle for dimension on compact subsets of the 2-torus which are invariant under a non-conformal expanding diagonal endomorphism. Condition (H) ensures that the invariant measures with full dimension are the equilibrium states of some potential function. This result applies to the problem of uniqueness of the measure with full dimension on the sofic affine-invariant sets.

引用

页码：1503 / 1528

页数：26

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