Co-induction in dynamical systems

DOI10.1017/S0143385711000083zbMath1263.37005OpenAlexW2163624483MaRDI QIDQ2908165

Anthony H. Dooley, Guohua Zhang

Publication date: 4 September 2012

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

Full work available at URL: https://doi.org/10.1017/s0143385711000083

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) General groups of measure-preserving transformations and dynamical systems (37A15)

Related Items (7)

ADDITIVITY PROPERTIES OF SOFIC ENTROPY AND MEASURES ON MODEL SPACES ⋮ Asymptotic pairs, stable sets and chaos in positive entropy systems ⋮ Local entropy theory for a countable discrete amenable group action ⋮ Classification of transitive group actions ⋮ The symbolic extension theory in topological dynamics ⋮ Local entropy theory of a random dynamical system ⋮ Conditional entropy and fiber entropy for amenable group actions

Cites Work

• \(T,T^{-1}\) transformation is not loosely Bernoulli
• Relative entropy tuples, relative u.p.e. and c.p.e. extensions
• Entropy and isomorphism theorems for actions of amenable groups
• The Abramov-Rokhlin entropy addition formula for amenable group actions
• New \(K\)-automorphisms and a problem of Kakutani
• Two nonisomorphic K-automorphisms all of whose powers beyond one are isomorphic
• Bernoulli shifts induced by K-automorphisms
• A simple characterization of the set of \(\mu\)-entropy pairs and applications
• Entropy and mixing for amenable group actions
• The spectrum of completely positive entropy actions of countable amenable groups
• A local variational relation and applications
• An example of a Kolmogorov automorphism that is not a Bernoulli shift
• A K-automorphism with no square root and Pinsker's conjecture
• An uncountable family of K-automorphisms
• A variation on the variational principle and applications to entropy pairs
• A local variational principle for conditional entropy
• Local entropy theory
• A $K$ counterexample machine
• A disjointness theorem involving topological entropy
• Entropy theory without a past
• Entropy pairs for a measure
• Non-Bernoulli systems with completely positive entropy
• Entropy theory from the orbital point of view

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