Entropy for expansive algebraic actions of residually finite groups

DOI10.1017/S0143385710000179zbMath1234.37010arXiv0909.4770OpenAlexW2964297208MaRDI QIDQ3012877

Lewis Phylip Bowen

Publication date: 7 July 2011

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

Full work available at URL: https://arxiv.org/abs/0909.4770

zbMATH Keywords

entropyperiodic pointresidually finite groupnon-amenable group

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35)

Related Items (28)

A remark on \(\mathbb{T}\)-valued cohomology groups of algebraic group actions ⋮ Fuglede-Kadison determinants and sofic entropy ⋮ The entropy of Gibbs measures on sofic groups ⋮ A survey of algebraic actions of the discrete Heisenberg group ⋮ An asymptotic equipartition property for measures on model spaces ⋮ Announce of an entropy formula for a class of actions coming from Gibbs measures ⋮ Combinatorial independence and sofic entropy ⋮ New examples of Bernoulli algebraic actions ⋮ Metric mean dimension for algebraic actions of Sofic groups ⋮ Free energy, Gibbs measures, and Glauber dynamics for nearest-neighbor interactions ⋮ Sofic entropy of Gaussian actions ⋮ ADDITIVITY PROPERTIES OF SOFIC ENTROPY AND MEASURES ON MODEL SPACES ⋮ Compact group automorphisms, addition formulas and Fuglede-Kadison determinants ⋮ Mean dimensions for partial actions ⋮ Entropy and the variational principle for actions of sofic groups ⋮ Weak equivalence to Bernoulli shifts for some algebraic actions ⋮ Max-min theorems for weak containment, square summable homoclinic points, and completely positive entropy ⋮ Homoclinic groups, IE groups, and expansive algebraic actions ⋮ Harmonic models and spanning forests of residually finite groups ⋮ Cost, \(\ell^2\)-Betti numbers and the sofic entropy of some algebraic actions ⋮ Examples in the entropy theory of countable group actions ⋮ Markovian properties of continuous group actions: algebraic actions, entropy and the homoclinic group ⋮ Local and doubly empirical convergence and the entropy of algebraic actions of sofic groups ⋮ Harmonic models and Bernoullicity ⋮ Fuglede-Kadison determinants for operators in the von Neumann algebra of an equivalence relation ⋮ Entropy, determinants, and $L^2$-torsion ⋮ Fractional free convolution powers ⋮ Entropy for partial actions of ℤ

Cites Work

• Mahler measure and entropy for commuting automorphisms of compact groups
• Determinant theory in finite factors
• Measure conjugacy invariants for actions of countable sofic groups
• Automorphisms of solenoids and p-adic entropy
• Almost Invariant Sets
• Amenability, Kazhdan's property T, strong ergodicity and invariant means for ergodic group-actions
• Expansive algebraic actions of discrete residually finite amenable groups and their entropy
• Amenable actions and almost invariant sets
• Fuglede–Kadison determinants and entropy for actions of discrete amenable groups

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