Embedding ℤk-actions in cubical shifts and ℤk-symbolic extensions

DOI10.1017/S0143385709001096zbMath1218.37013MaRDI QIDQ3002594

Yonatan Gutman

Publication date: 20 May 2011

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

zbMATH Keywords

embedding theoremtopological entropymean dimensionsymbolic extension

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Related Items (25)

Mean dimension and Jaworski-type theorems ⋮ Mean dimension of full shifts ⋮ Mean dimension, mean rank, and von Neumann-Lück rank ⋮ Mean dimension of \({\mathbb{Z}^k}\)-actions ⋮ Comparison radius and mean topological dimension: Rokhlin property, comparison of open sets, and subhomogeneous C*-algebras ⋮ Mean dimension and a sharp embedding theorem: extensions of aperiodic subshifts ⋮ Embedding minimal dynamical systems into Hilbert cubes ⋮ On embeddings of extensions of almost finite actions into cubical shifts ⋮ Mean dimension of the dynamical system of Brody curves ⋮ Sofic mean dimension ⋮ Embedding topological dynamical systems with periodic points in cubical shifts ⋮ Dynamical correspondences of \(L^2\)-Betti numbers ⋮ Expansive multiparameter actions and mean dimension ⋮ Mean dimension and an embedding theorem for real flows ⋮ Tail variational principle for a countable discrete amenable group action ⋮ Minimal subshifts of arbitrary mean topological dimension ⋮ Mean dimension and an embedding problem: an example ⋮ Almost finiteness and the small boundary property ⋮ 𝒵-stability of transformation group C*-algebras ⋮ Generic homeomorphisms have full metric mean dimension ⋮ Sofic mean length ⋮ The symbolic extension theory in topological dynamics ⋮ The Rokhlin dimension of topological ℤ^m -actions ⋮ Conditional mean dimension ⋮ Symbolic Extensions of Amenable Group Actions and the Comparison Property

Cites Work

• Entropy structure
• Mean dimension, small entropy factors and an embedding theorem
• The entropy theory of symbolic extensions
• Mean topological dimension
• Topological invariants of dynamical systems and spaces of holomorphic maps. I.
• Entropy of a symbolic extension of a dynamical system
• Residual entropy, conditional entropy and subshift covers
• Can one always lower topological entropy?
• Morphisms from non-periodic \mathbb{Z}^{2} subshifts I: constructing embeddings from homomorphisms

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