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The finitary isomorphism theorem for Markov shifts. (English) Zbl 0407.28010


MSC:

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

[1] M. A. Akcoglu, A. del Junco, and M. Rahe, Finitary codes between Markov processes, Z. Wahrsch. Verw. Gebiete 47 (1979), no. 3, 305 – 314. · Zbl 0403.28017
[2] R. L. Adler, P. Shields, and M. Smorodinsky, Irreducible Markov shifts, Ann. Math. Statist. 43 (1972), 1027 – 1029. · Zbl 0244.60053
[3] Roy L. Adler and Brian Marcus, Topological entropy and equivalence of dynamical systems, Mem. Amer. Math. Soc. 20 (1979), no. 219, iv+84. · Zbl 0412.54050
[4] Roy L. Adler and Benjamin Weiss, Similarity of automorphisms of the torus, Memoirs of the American Mathematical Society, No. 98, American Mathematical Society, Providence, R.I., 1970. · Zbl 0195.06104
[5] Rufus Bowen, Smooth partitions of Anosov diffeomorphisms are weak Bernoulli, Israel J. Math. 21 (1975), no. 2-3, 95 – 100. Conference on Ergodic Theory and Topological Dynamics (Kibbutz Lavi, 1974). · Zbl 0315.58020
[6] Donald Ornstein, Two Bernoulli shifts with infinite entropy are isomorphic, Advances in Math. 5 (1970), 339 – 348 (1970). , https://doi.org/10.1016/0001-8708(70)90008-3 Donald Ornstein, Factors of Bernoulli shifts are Bernoulli shifts, Advances in Math. 5 (1970), 349 – 364 (1970). , https://doi.org/10.1016/0001-8708(70)90009-5 N. A. Friedman and D. S. Ornstein, On isomorphism of weak Bernoulli transformations, Advances in Math. 5 (1970), 365 – 394 (1970). · Zbl 0203.05801
[7] M. Keane and M. Smorodinsky, A class of finitary codes, Israel J. Math. 26 (1977), no. 3-4, 352 – 371. · Zbl 0357.94012
[8] Michael Keane and Meir Smorodinsky, Bernoulli schemes of the same entropy are finitarily isomorphic, Ann. of Math. (2) 109 (1979), no. 2, 397 – 406. · Zbl 0405.28017
[9] M. Smorodinsky, \?-automorphisms are Bernoulli shifts, Acta Math. Acad. Sci. Hungar. 24 (1973), 273 – 278. · Zbl 0268.28007
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