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Ergodic automorphisms of \(T^ n\) are Bernoulli shifts. (English) Zbl 0219.28014


MSC:

28D05 Measure-preserving transformations
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References:

[1] R. L. Adler, and B. Weiss,Similarity of automorphisms of the torus, Mem. Amer. Math. Soc. No. 98 (1970). · Zbl 0195.06104
[2] D. S. Ornstein,Imbedding Bernoulli shifts in flows, Contribution to Ergodic Theory and Probability, pp. 178-218, Springer-Verlag, 1970. · Zbl 0227.28013
[3] Ornstein, D. S., Two Bernoulli shifts with infinite entropy are isomorphic, Advances in Math., 5, 339-348 (1970) · Zbl 0227.28014 · doi:10.1016/0001-8708(70)90008-3
[4] Rohlin, V. A., Metric properties of endomorphisms of commutative groups, Amer. Math. Soc. translations Series 2, 64, 244-272 (1967) · Zbl 0183.03602
[5] Rohlin, V. A., Exact endomorphisms of a Lebesuge sapce, Amer. Math. Soc. translations Series 2, 39, 1-36 (1969) · Zbl 0154.15703
[6] Sinai, Ya. G., Markov partitions and c-diffeomorphisms, Functional Anal. Appl., 2, 161-82 (1968) · Zbl 0182.55003 · doi:10.1007/BF01075361
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