The finitary isomorphism theorem for Markov shifts

DOI10.1090/S0273-0979-1979-14633-0zbMath0407.28010MaRDI QIDQ4193697

Meir Smorodinsky, Michael S. Keane

Publication date: 1979

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

EntropyDiscrete State Space Stationary ProcessesFinitary IsomorphismHyperbolic AutomorphismMarkov ShiftsToral Automorphism

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Entropy and other invariants (28D20) Dynamical systems with hyperbolic behavior (37D99)

Related Items (9)

Unnamed Item ⋮ Unnamed Item ⋮ The Morse minimal system is nearly continuously Kakutani equivalent to the binary odometer ⋮ Finitary isomorphisms of irreducible Markov shifts ⋮ Ergodic group automorphisms are exponentially recurrent ⋮ Every Borel automorphism without finite invariant measures admits a two-set generator ⋮ Any two irrational rotations are nearly continuously Kakutani equivalent ⋮ The Bernoulli property for expansive \(\mathbb Z^ 2\) actions on compact groups ⋮ Finitary coding of Markov random fields

Cites Work

• Smooth partitions of Anosov diffeomorphisms are weak Bernoulli
• A class of finitary codes
• Bernoulli schemes of the same entropy are finitarily isomorphic
• On isomorphism of weak Bernoulli transformations
• β-automorphisms are Bernoulli shifts
• Finitary codes between Markov processes
• Topological entropy and equivalence of dynamical systems
• Similarity of automorphisms of the torus
• Irreducible Markov Shifts

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