Ergodic automorphisms of compact metric groups are isomorphic to Bernoulli shifts
International conference on dynamical systems in mathematical physics, Astérisque, no. 40 (1976), pp. 5-10. 
@incollection{AST_1976__40__5_0,
     author = {Aoki, Nobuo},
     title = {Ergodic automorphisms of compact metric groups are isomorphic to {Bernoulli} shifts},
     booktitle = {International conference on dynamical systems in mathematical physics},
     series = {Ast\'erisque},
     pages = {5--10},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {40},
     year = {1976},
     mrnumber = {463398},
     zbl = {0355.28011},
     language = {en},
     url = {http://www.numdam.org/item/AST_1976__40__5_0/}
}
TY  - CHAP
AU  - Aoki, Nobuo
TI  - Ergodic automorphisms of compact metric groups are isomorphic to Bernoulli shifts
BT  - International conference on dynamical systems in mathematical physics
AU  - Collectif
T3  - Astérisque
PY  - 1976
SP  - 5
EP  - 10
IS  - 40
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_1976__40__5_0/
LA  - en
ID  - AST_1976__40__5_0
ER  - 
%0 Book Section
%A Aoki, Nobuo
%T Ergodic automorphisms of compact metric groups are isomorphic to Bernoulli shifts
%B International conference on dynamical systems in mathematical physics
%A Collectif
%S Astérisque
%D 1976
%P 5-10
%N 40
%I Société mathématique de France
%U http://www.numdam.org/item/AST_1976__40__5_0/
%G en
%F AST_1976__40__5_0
Aoki, Nobuo. Ergodic automorphisms of compact metric groups are isomorphic to Bernoulli shifts, dans International conference on dynamical systems in mathematical physics, Astérisque, no. 40 (1976), pp. 5-10. http://www.numdam.org/item/AST_1976__40__5_0/

[1] L. M. Abramov, The entropy of an automorphism of a solenidal group, Theory of Prob. and its Appl. 4 (1959), 231-236. | DOI | MR

[2] R. L. Adler and B. Weiss, Similarity of automorphisms of the torus, Mem. Amer. Soc. 98 (1970). | MR | Zbl

[3] N. Aoki and H. Totoki, Ergodic automorphisms of T are Bernoulli transformations, Publ. RIMS, Kyoto Univ. 10 (1975), 535-544. | DOI | MR | Zbl

[4] D. Z. Arov, The computation of entropy for one class of group endomorphisms, Zap. Meh. Mat. Fak. Kharov, Math. Obshck 30 (1964), 48-69. | MR

[5] K. R. Berg, Entropy of torus automorphisms, Topological Dynamics (edited by W.H. Gottschalk and F. Hahn), Benjamin New York, (1969), 516-519.

[6] D. Lind, Ergodic automorphisms of the infinite torus are Bernoulli, Israel J. Math. 10 (1974), 186-195. | MR | Zbl

[7] N. A. Friedman and D. S. Ornstein, On isomorphism of weak Bernoulli transformations, Advances in Math. 5 (1971), 365-394. | DOI | MR | Zbl

[8] P. R. Halmos and H. Samelson, On monothetic groups, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 254-258. | DOI | MR | Zbl

[9] G. Hochschild, The structure of Lie Groups, Holden-Day, San Francisco, 1965. | MR | Zbl

[10] I. Kaplansky, Groups with representations of bounded degree, Canad. J. Math. 1 (1949) ; 105-112. | DOI | MR | Zbl

[11] Y. Katznelson, Ergodic automorphisms of T n are Bernoulli shifts, Israel J. Math. 10 (1971), 186-195. | DOI | MR | Zbl

[12] A. G. Kurosch, The theory of Groups I, Chelsea, New York, 1960. | MR

[13] D. S. Ornstein, Bernoulli shifts with the same entropy are isomorphic, Advances in Math. 4 (1970), 337-352. | DOI | MR | Zbl

[14] D. S. Ornstein, Two Bernoulli shifts with infinite entropy are isomorphic, Advances in Math. 5 (1971), 339-348. | DOI | MR | Zbl

[15] D. S. Ornstein, Factors of Bernoulli shifts are Bernoulli shifts, Advances in Math. 5 (1971), 349-364. | DOI | MR | Zbl

[16] W. Parry, Intrinsic Markov chains, Trans. Amer. Math. Soc. 112 (1964), 55-66. | DOI | MR | Zbl

[17] M. S. Pinsker, Dynamical systems with completely positive and zero entroy, Soviet Mathematics Doklady, 1 (1960), 937-938. | MR | Zbl

[18] L. Pontjagin, Topological Groups, Princeton Univ. Press. Princeton, 1946.

[19] V. A. Rohlin, Metric properties of endomorphisms of compact commutative groups, Amer. Math. Soc. Transl. 64 (1967), 244-272. | Zbl

[20] V. A. Rohlin, On the fundamental ideas of measure theory. Amer. Math. Soc. Transl. 10 (1962), 1-54.

[21] V. A. Rohlin, Exact endomorphisms of a Lebesgue space, Amer. Math. Soc. Transl. 39 (1969), 1-36. | Zbl

[22] V. A. Rohlin, Selected topics from the metric theory of dynamical systems, Amer. Math. Soc. Transl. 49 (1966), 171-240. | Zbl

[23] Ya. G. Sinai, Markov partitions and C-diffeomorphisms, Fanc. Anal. and its Appl. 2 (1968), 61-82. | DOI | Zbl

[24] Ya. G. Sinai, On the concept of entropy of a dynamical system, Dokl. Akad. Nauk. 124 (1959), 768-771. | MR | Zbl

[25] H. Totoki, Introduction to Ergodic Theory, Kyoritsu Shuppan, Tokyo, 1971 (in Japanese).

[26] H. Totoki, Ergodic Theory, Lecture notes series 14, Aarhus Univ. 1969. | MR

[27] A. Wiel, L'intégration dans les Groups Topologique et ses Applications, Actualités Sci. Indust. 869, Hermann, Paris, 1940 | JFM | MR | Zbl

A. Wiel, L'intégration dans les Groups Topologique et ses Applications, Actualités Sci. Indust. 869, Hermann, Paris, 2nd ed. 1951.

[28] S. A. Yuzvinskii, Metric properties of endomorphisms of compact groups. Amer. Math. Transl. 66 (1968), 63-98. | Zbl