Minimal models for noninvertible and not uniquely ergodic systems

DOI10.1007/BF02773826zbMath1131.37012MaRDI QIDQ2472742

Tomasz Downarowicz

Publication date: 22 February 2008

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Borel isomorphisminvariant measuresminimal syste

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Symbolic dynamics (37B10) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Related Items (20)

Measure of noninvertibility of minimal maps ⋮ Mean dimension and Jaworski-type theorems ⋮ Mean dimension of \({\mathbb{Z}^k}\)-actions ⋮ Dynamics in dimension zero A survey ⋮ Embedding asymptotically expansive systems ⋮ Bowen’s equations for upper metric mean dimension with potential ⋮ Embedding theorems for discrete dynamical systems and topological flows ⋮ Universal systems for entropy intervals ⋮ Faces of simplices of invariant measures for actions of amenable groups ⋮ Embedding topological dynamical systems with periodic points in cubical shifts ⋮ Non-existence of a universal zero-entropy system ⋮ Bounded complexity, mean equicontinuity and discrete spectrum ⋮ Invariant measures for Cantor dynamical systems ⋮ Zero-dimensional isomorphic dynamical models ⋮ Faces of simplexes of invariant measures ⋮ Topological realizations of families of ergodic automorphisms, multitowers and orbit equivalence ⋮ Invariant measures on stationary Bratteli diagrams ⋮ Ergodic universality of some topological dynamical systems ⋮ Exact number of ergodic invariant measures for Bratteli diagrams ⋮ Dynamic asymptotic dimension for actions of virtually cyclic groups

Cites Work

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• Entropy structure
• Strictly ergodic models for non-invertible transformations
• Mean dimension, small entropy factors and an embedding theorem
• Topological realizations of families of ergodic automorphisms, multitowers and orbit equivalence
• Fiber entropy and conditional variational principles in compact non-metrizable spaces
• Zero-dimensional covers of finite dimensional dynamical systems

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