A necessary and sufficient condition for a matrix equilibrium state to be mixing

DOI10.1017/etds.2017.122zbMath1423.37008arXiv1612.01761OpenAlexW2950597830MaRDI QIDQ4968756

Ian D. Morris

Publication date: 9 July 2019

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

Full work available at URL: https://arxiv.org/abs/1612.01761

zbMATH Keywords

equilibrium statesshift spacesBernoulli measureHölder-continuous potentials

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35)

Related Items (6)

Some observations on K\"aenm\"aki measures ⋮ Bernoulli property of subadditive equilibrium states ⋮ The weak Bernoulli property for matrix Gibbs states ⋮ Totally ergodic generalised matrix equilibrium states have the Bernoulli property ⋮ Equilibrium states of generalised singular value potentials and applications to affine iterated function systems ⋮ TheK-property for subadditive equilibrium states

Cites Work

• Equilibrium states of the pressure function for products of matrices
• The thermodynamic formalism for sub-additive potentials
• Falconer's formula for the Hausdorff dimension of a self-affine set in R²
• Dimension of self-affine sets for fixed translation vectors
• Planar self-affine sets with equal Hausdorff, box and affinity dimensions
• On equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems
• Unnamed Item

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