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

DOI10.1017/S0143385709000546zbMath1221.37007MaRDI QIDQ3058063

Eric Olivier

Publication date: 18 November 2010

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

2-torusuniqueness of measureinvariant measure with full dimensionsofic affine-invariant set

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Dimension theory of smooth dynamical systems (37C45)

Related Items (8)

Dimension of self-affine sets with holes ⋮ Equilibrium states for factor maps between subshifts ⋮ Measures of Full Dimension on Self-Affine Graphs ⋮ Dimension spectrum for sofic systems ⋮ On the uniqueness of an ergodic measure of full dimension for non-conformal repellers ⋮ On factors of Gibbs measures for almost additive potentials ⋮ APPLICATIONS OF A RELATIVE VARIATIONAL PRINCIPLE TO DIMENSIONS OF NONCONFORMAL EXPANDING MAPS ⋮ On a class of sofic affine invariant subsets of the 2-torus related to an Erdős problem

Cites Work

• Unnamed Item
• Unnamed Item
• Some exceptional phenomena in multifractal formalism. I
• Chains with infinite connections: Uniqueness and Markov representation
• Equivalence of Gibbs and equilibrium states for homeomorphisms satisfying expansiveness and specification
• Ergodic theory on compact spaces
• Subshifts of finite type and sofic systems
• Hausdorff dimensions of sofic affine-invariant sets
• Gibbs measures for fibred systems
• The metric entropy of diffeomorphisms. II: Relations between entropy, exponents and dimension
• Non-negative matrices and Markov chains.
• A modified multifractal formalism for a class of self-similar measures with overlap
• Some exceptional phenomena in multifractal formalism. II
• Strongly mixing g-measures
• Invariant measures of full dimension for some expanding maps
• On the relative variational principle for fibre expanding maps
• The Hausdorff dimension of general Sierpiński carpets
• Dimensions of compact invariant sets of some expanding maps
• Dimension, entropy and Lyapunov exponents
• The dimension of self-affine fractals II
• Thermodynamic formalism of maps satisfying positive expansiveness and specification
• Some systems with unique equilibrium states
• A Relativised Variational Principle for Continuous Transformations
• Uniqueness of equilibrium measures for countable Markov shifts and multidimensional piecewise expanding maps
• Multifractal analysis of weak Gibbs measures and phase transition—application to some Bernoulli convolutions
• Repellers for real analytic maps
• Existence of Gibbs measures for countable Markov shifts
• Measures of full dimension on affine-invariant sets
• Thermodynamic formalism for countable Markov shifts
• A variational principle for the dimension for a class of non-conformal repellers
• Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• Thermodynamic formalism for null recurrent potentials
• Gibbs states on the symbolic space over an infinite alphabet
• Multifractal structure of convolution of the Cantor measure

This page was built for publication: Uniqueness of the measure with full dimension on sofic affine-invariant subsets of the 2-torus