Mean dimension of \({\mathbb{Z}^k}\)-actions
From MaRDI portal
Publication:311140
DOI10.1007/S00039-016-0372-9zbMath1378.37056arXiv1510.01605OpenAlexW2263898306MaRDI QIDQ311140
Elon Lindenstrauss, Yonatan Gutman, Masaki Tsukamoto
Publication date: 29 September 2016
Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1510.01605
Dynamics induced by group actions other than (mathbb{Z}) and (mathbb{R}), and (mathbb{C}) (37C85) Topological entropy (37B40)
Related Items (37)
Mean dimension of full shifts ⋮ Mean dimension and a non-embeddable example for amenable group actions ⋮ Shadowing and mixing on systems of countable group actions ⋮ Mean dimension theory in symbolic dynamics for finitely generated amenable groups ⋮ Polynomial growth, comparison, and the small boundary property ⋮ Comparison radius and mean topological dimension: Rokhlin property, comparison of open sets, and subhomogeneous C*-algebras ⋮ Variational principles for amenable metric mean dimensions ⋮ Embedding minimal dynamical systems into Hilbert cubes ⋮ 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 ⋮ Invariant ergodic measures and the classification of crossed product \(C^{\ast}\)-algebras ⋮ Finite mean dimension and marker property ⋮ Double variational principle for mean dimensions with sub-additive potentials ⋮ Mean dimension of natural extension of algebraic systems ⋮ On embeddings of extensions of almost finite actions into cubical shifts ⋮ Dynamical comparison and \(\mathcal{Z} \)-stability for crossed products of simple \(C^\ast \)-algebras ⋮ The embedding problem in topological dynamics and Takens’ theorem ⋮ Weighted mean topological dimension ⋮ Dynamical correspondences of \(L^2\)-Betti numbers ⋮ Expansive multiparameter actions and mean dimension ⋮ Mean dimension and an embedding theorem for real flows ⋮ Upper metric mean dimensions with potential on subsets ⋮ Amenable upper mean dimensions ⋮ Double variational principle for mean dimension with potential ⋮ Almost finiteness and the small boundary property ⋮ 𝒵-stability of transformation group C*-algebras ⋮ Generic homeomorphisms have full metric mean dimension ⋮ Upper metric mean dimensions for impulsive semi-flows ⋮ Double variational principle for mean dimension ⋮ Sofic mean length ⋮ The symbolic extension theory in topological dynamics ⋮ Symbolic dynamics in mean dimension theory ⋮ Application of signal analysis to the embedding problem of \({\mathbb{Z}}^k\)-actions ⋮ Around the variational principle for metric mean dimension ⋮ Conditional mean dimension ⋮ Directional mean dimension and continuum-wise expansive ℤ^{𝕜}-actions
Cites Work
- Unnamed Item
- Minimal systems of arbitrary large mean topological dimension
- Entropy and isomorphism theorems for actions of amenable groups
- Mean dimension, small entropy factors and an embedding theorem
- Lowering topological entropy
- Mean topological dimension
- Topological invariants of dynamical systems and spaces of holomorphic maps. I.
- Mean dimension and an embedding problem: an example
- Sofic mean dimension
- Minimal models for noninvertible and not uniquely ergodic systems
- A proof of Beboutov's theorem
- Mean dimension and a sharp embedding theorem: extensions of aperiodic subshifts
- Embedding topological dynamical systems with periodic points in cubical shifts
- Embedding ℤk-actions in cubical shifts and ℤk-symbolic extensions
- Morphisms from non-periodic $\mathbb{Z}^2$ subshifts II: constructing homomorphisms to square-filling mixing shifts of finite type
- Mean dimension and Jaworski-type theorems
- Can one always lower topological entropy?
- Morphisms from non-periodic \mathbb{Z}^{2} subshifts I: constructing embeddings from homomorphisms
- On the subsystems of topological Markov chains
This page was built for publication: Mean dimension of \({\mathbb{Z}^k}\)-actions