Embedding minimal dynamical systems into Hilbert cubes

DOI10.1007/s00222-019-00942-wzbMath1444.37010arXiv1511.01802OpenAlexW2998243751WikidataQ126460596 ScholiaQ126460596MaRDI QIDQ2187253

Masaki Tsukamoto, Yonatan Gutman

Publication date: 2 June 2020

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.01802

zbMATH Keywords

harmonic analysisHilbert cubeshift actiondynamical coding techniques

Mathematics Subject Classification ID

Dimension theory in general topology (54F45) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Dimension theory of smooth dynamical systems (37C45) Dynamics in general topological spaces (37B02)

Related Items (27)

Mean dimension of Bernstein spaces and universal real flows ⋮ Mean dimension of full shifts ⋮ Mean dimension and a non-embeddable example for amenable group actions ⋮ Mean dimension theory in symbolic dynamics for finitely generated amenable groups ⋮ Embedding asymptotically expansive systems ⋮ Mean dimension and metric mean dimension for non-autonomous dynamical systems ⋮ Variational principle for metric mean dimension with potential ⋮ \(G\)-index, topological dynamics and the marker property ⋮ Bowen’s equations for upper metric mean dimension with potential ⋮ Embedding theorems for discrete dynamical systems and topological flows ⋮ Metric mean dimension via preimage structures ⋮ Finite mean dimension and marker property ⋮ Double variational principle for mean dimensions with sub-additive potentials ⋮ On embeddings of extensions of almost finite actions into cubical shifts ⋮ The Hilbert cube contains a minimal subshift of full mean dimension ⋮ Weighted mean topological dimension ⋮ Dynamical correspondences of \(L^2\)-Betti numbers ⋮ Expansive multiparameter actions and mean dimension ⋮ Genericity of continuous maps with positive metric mean dimension ⋮ Double variational principle for mean dimension with potential ⋮ Double variational principle for mean dimension ⋮ Symbolic dynamics in mean dimension theory ⋮ Mean topological dimension for random bundle transformations ⋮ Application of signal analysis to the embedding problem of \({\mathbb{Z}}^k\)-actions ⋮ Around the variational principle for metric mean dimension ⋮ Directional mean dimension and continuum-wise expansive ℤ^{𝕜}-actions ⋮ Symbolic Extensions of Amenable Group Actions and the Comparison Property

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