@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] The entropy of an automorphism of a solenidal group, Theory of Prob. and its Appl. 4 (1959), 231-236. | DOI | MR
,[2] Similarity of automorphisms of the torus, Mem. Amer. Soc. 98 (1970). | MR | Zbl
and ,[3] Ergodic automorphisms of are Bernoulli transformations, Publ. RIMS, Kyoto Univ. 10 (1975), 535-544. | DOI | MR | Zbl
and ,[4] The computation of entropy for one class of group endomorphisms, Zap. Meh. Mat. Fak. Kharov, Math. Obshck 30 (1964), 48-69. | MR
,[5] Entropy of torus automorphisms, Topological Dynamics (edited by W.H. Gottschalk and F. Hahn), Benjamin New York, (1969), 516-519.
,[6] Ergodic automorphisms of the infinite torus are Bernoulli, Israel J. Math. 10 (1974), 186-195. | MR | Zbl
,[7] On isomorphism of weak Bernoulli transformations, Advances in Math. 5 (1971), 365-394. | DOI | MR | Zbl
and ,[8] On monothetic groups, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 254-258. | DOI | MR | Zbl
and ,[9] The structure of Lie Groups, Holden-Day, San Francisco, 1965. | MR | Zbl
,[10] Groups with representations of bounded degree, Canad. J. Math. 1 (1949) ; 105-112. | DOI | MR | Zbl
,[11] Ergodic automorphisms of are Bernoulli shifts, Israel J. Math. 10 (1971), 186-195. | DOI | MR | Zbl
,[12] The theory of Groups I, Chelsea, New York, 1960. | MR
,[13] Bernoulli shifts with the same entropy are isomorphic, Advances in Math. 4 (1970), 337-352. | DOI | MR | Zbl
,[14] Two Bernoulli shifts with infinite entropy are isomorphic, Advances in Math. 5 (1971), 339-348. | DOI | MR | Zbl
,[15] Factors of Bernoulli shifts are Bernoulli shifts, Advances in Math. 5 (1971), 349-364. | DOI | MR | Zbl
,[16] Intrinsic Markov chains, Trans. Amer. Math. Soc. 112 (1964), 55-66. | DOI | MR | Zbl
,[17] Dynamical systems with completely positive and zero entroy, Soviet Mathematics Doklady, 1 (1960), 937-938. | MR | Zbl
,[18] Topological Groups, Princeton Univ. Press. Princeton, 1946.
,[19] Metric properties of endomorphisms of compact commutative groups, Amer. Math. Soc. Transl. 64 (1967), 244-272. | Zbl
,[20] On the fundamental ideas of measure theory. Amer. Math. Soc. Transl. 10 (1962), 1-54.
,[21] Exact endomorphisms of a Lebesgue space, Amer. Math. Soc. Transl. 39 (1969), 1-36. | Zbl
,[22] Selected topics from the metric theory of dynamical systems, Amer. Math. Soc. Transl. 49 (1966), 171-240. | Zbl
,[23] Markov partitions and -diffeomorphisms, Fanc. Anal. and its Appl. 2 (1968), 61-82. | DOI | Zbl
,[24] On the concept of entropy of a dynamical system, Dokl. Akad. Nauk. 124 (1959), 768-771. | MR | Zbl
,[25] Introduction to Ergodic Theory, Kyoritsu Shuppan, Tokyo, 1971 (in Japanese).
,[26] Ergodic Theory, Lecture notes series 14, Aarhus Univ. 1969. | MR
,[27] L'intégration dans les Groups Topologique et ses Applications, Actualités Sci. Indust. 869, Hermann, Paris, 1940 | JFM | MR | Zbl
,L'intégration dans les Groups Topologique et ses Applications, Actualités Sci. Indust. 869, Hermann, Paris, 2nd ed. 1951.
,[28] Metric properties of endomorphisms of compact groups. Amer. Math. Transl. 66 (1968), 63-98. | Zbl
,