Mean dimension theory in symbolic dynamics for finitely generated amenable groups

DOI10.3934/dcds.2022050zbMath1502.37023arXiv2103.14817OpenAlexW3144035644MaRDI QIDQ2158210

Xiaoyao Zhou, Yunping Wang, Ercai Chen

Publication date: 26 July 2022

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.14817

zbMATH Keywords

subshiftmetric mean dimensionpolynomial growth grouprate distortion dimensionmean Hausdorff dimension

Mathematics Subject Classification ID

Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Topological entropy (37B40) Dimension theory of smooth dynamical systems (37C45)

Cites Work

• Mean dimension of \({\mathbb{Z}^k}\)-actions
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• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
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• Embedding minimal dynamical systems into Hilbert cubes
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• Application of signal analysis to the embedding problem of \({\mathbb{Z}}^k\)-actions
• Topological dimension and dynamical systems. Translated from the French by the author
• Symbolic dynamics: entropy = dimension = complexity
• Variational principles for amenable metric mean dimensions
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• The rate-distortion dimension of sets and measures
• Expansive multiparameter actions and mean dimension
• Symbolic dynamics in mean dimension theory
• Topological Entropy
• From Rate Distortion Theory to Metric Mean Dimension: Variational Principle
• Elements of Information Theory
• Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation
• The Degree of Polynomial Growth of Finitely Generated Nilpotent Groups
• Ergodic Theory

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