Minimal systems with finitely many ergodic measures

DOI10.1016/j.jfa.2021.109000zbMath1465.37006arXiv2002.08792OpenAlexW3138774941MaRDI QIDQ2020080

Song Shao, Wen Huang, Zhengxing Lian, Xiang Dong Ye

Publication date: 23 April 2021

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.08792

zbMATH Keywords

entropyindependent setamenable groupergodic measure

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Topological entropy (37B40) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) General groups of measure-preserving transformations and dynamical systems (37A15)

Related Items

On the minimum ergodic average and minimal systems ⋮ Almost proximal extensions of minimal flows ⋮ Sequence entropy tuples and mean sensitive tuples

Cites Work

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• Combinatorial lemmas and applications to dynamics
• A unique ergodicity of minimal symbolic flows with linear block growth
• Highly proximal and generalized almost finite extensions of minimal sets
• A point distal transformation of the torus
• Pointwise theorems for amenable groups.
• The structure of tame minimal dynamical systems for general groups
• Counting generic measures for a subshift of linear growth
• The logarithmic Sarnak conjecture for ergodic weights
• Independence in topological and \(C^*\)-dynamics
• Stronger version sensitivity, almost finite to one extension and maximal pattern entropy
• Finite rank Bratteli diagrams: Structure of invariant measures
• Homomorphisms of Transformation Groups
• A Semigroup Associated With a Transformation Group
• Tame systems and scrambled pairs under an Abelian group action
• On sensitive sets in topological dynamics
• Sequence Entropy and Subsequence Generators
• Topological Sequence Entropy
• A disjointness theorem involving topological entropy
• Null systems and sequence entropy pairs
• Analogues of Auslander–Yorke theorems for multi-sensitivity
• Finite Extensions of Minimal Transformation Groups
• The structure of tame minimal dynamical systems
• Structure of bounded topological-sequence-entropy minimal systems
• On tame dynamical systems
• ON METRIC INVARIANTS OF ENTROPY TYPE
• Groups of Automorphisms of Borel Spaces
• Point-Distal Flows
• Proximity Relations in Transformation Groups
• Interplay between finite topological rank minimal Cantor systems, 𝒮-adic subshifts and their complexity
• Irregular model sets and tame dynamics