Some new results in the Kolmogorov-Sinai theory of entropy and ergodic theory
HTML articles powered by AMS MathViewer
- by Donald S. Ornstein PDF
- Bull. Amer. Math. Soc. 77 (1971), 878-890
References
- Paul R. Halmos, Lectures on ergodic theory, Chelsea Publishing Co., New York, 1960. MR 0111817
- Patrick Billingsley, Ergodic theory and information, John Wiley & Sons, Inc., New York-London-Sydney, 1965. MR 0192027
- A. N. Kolmogorov, A new metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces, Dokl. Akad. Nauk SSSR (N.S.) 119 (1958), 861–864 (Russian). MR 0103254
- A. N. Kolmogorov, A new metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces, Dokl. Akad. Nauk SSSR (N.S.) 119 (1958), 861–864 (Russian). MR 0103254
- Ja. G. Sinaĭ, A weak isomorphism of transformations with invariant measure, Dokl. Akad. Nauk SSSR 147 (1962), 797–800 (Russian). MR 0161960
- L. D. Mešalkin, A case of isomorphism of Bernoulli schemes, Dokl. Akad. Nauk SSSR 128 (1959), 41–44 (Russian). MR 0110782
- Donald Ornstein, Bernoulli shifts with the same entropy are isomorphic, Advances in Math. 4 (1970), 337–352. MR 257322, DOI 10.1016/0001-8708(70)90029-0
- Meir Smorodinsky, On Ornstein’s isomorphism theorem for Bernoulli shifts, Advances in Math. 9 (1972), 1–9. MR 299756, DOI 10.1016/0001-8708(72)90027-8
- Donald Ornstein, Two Bernoulli shifts with infinite entropy are isomorphic, Advances in Math. 5 (1970), 339–348 (1970). MR 274716, DOI 10.1016/0001-8708(70)90008-3
- Donald Ornstein, Two Bernoulli shifts with infinite entropy are isomorphic, Advances in Math. 5 (1970), 339–348 (1970). MR 274716, DOI 10.1016/0001-8708(70)90008-3
- D. S. Ornstein, Imbedding Bernoulli shifts in flows, Contributions to Ergodic Theory and Probability (Proc. Conf., Ohio State Univ., Columbus, Ohio, 1970) Springer, Berlin, 1970, pp. 178–218. MR 0272985
- Donald S. Ornstein, An example of a Kolmogorov automorphism that is not a Bernoulli shift, Advances in Math. 10 (1973), 49–62. MR 316682, DOI 10.1016/0001-8708(73)90097-2
- Donald Ornstein, Two Bernoulli shifts with infinite entropy are isomorphic, Advances in Math. 5 (1970), 339–348 (1970). MR 274716, DOI 10.1016/0001-8708(70)90008-3
- Donald S. Ornstein, An application of ergodic theory to probability theory, Ann. Probability 1 (1973), no. 1, 43–65. MR 348831, DOI 10.1098/rsnr.1972.0008
- V. A. Rohlin and Ja. G. Sinaĭ, The structure and properties of invariant measurable partitions, Dokl. Akad. Nauk SSSR 141 (1961), 1038–1041 (Russian). MR 0152629 16. S. Ito, H. Murata and H. Totoki, A remark on the isomorphism theorem for weak Bernoulli transformations (to appear).
- Robert McCabe and Paul Shields, A class of Markov shifts which are Bernoulli shifts, Advances in Math. 6 (1971), 323–328. MR 291858, DOI 10.1016/0001-8708(71)90019-3 18. M. Smorodinsky, A partition for a Bernoulli shift that is not weak Bernoulli (to appear).
- R. L. Adler and B. Weiss, Entropy, a complete metric invariant for automorphisms of the torus, Proc. Nat. Acad. Sci. U.S.A. 57 (1967), 1573–1576. MR 212156, DOI 10.1073/pnas.57.6.1573
- Ja. G. Sinaĭ, Markov partitions and U-diffeomorphisms, Funkcional. Anal. i Priložen 2 (1968), no. 1, 64–89 (Russian). MR 0233038
- Yitzhak Katznelson, Ergodic automorphisms of $T^{n}$ are Bernoulli shifts, Israel J. Math. 10 (1971), 186–195. MR 294602, DOI 10.1007/BF02771569
- Rufus Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401–414. MR 274707, DOI 10.1090/S0002-9947-1971-0274707-X
- V. A. Rohlin, Metric properties of endomorphisms of compact commutative groups, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 867–874 (Russian). MR 0168697
- S. A. Juzvinskiĭ, Metric properties of the endomorphisms of compact groups, Izv. Akad. Nauk SSSR Ser. Mat. 29 (1965), 1295–1328 (Russian). MR 0194588
- A. N. Kolmogorov, Théorie générale des systèmes dynamiques et mécanique classique, Proceedings of the International Congress of Mathematicians, Amsterdam, 1954, Vol. 1, Erven P. Noordhoff N. V., Groningen; North-Holland Publishing Co., Amsterdam, 1957, pp. 315–333 (French). MR 0097598
- V. I. Arnol′d and A. Avez, Ergodic problems of classical mechanics, W. A. Benjamin, Inc., New York-Amsterdam, 1968. Translated from the French by A. Avez. MR 0232910
- Ja. G. Sinaĭ, On the foundations of the ergodic hypothesis for a dynamical system of statistical mechanics, Soviet Math. Dokl. 4 (1963), 1818–1822. MR 0214727 28. D. S. Ornstein, A mixing transformation for which Pinsker’s conjecture fails (to appear). 29. D. S. Ornstein, A K-automorphism with no square root and Pinsker’s conjecture (to appear).
- Donald S. Ornstein, The isomorphism theorem for Bernoulli flows, Advances in Math. 10 (1973), 124–142. MR 318452, DOI 10.1016/0001-8708(73)90101-1
Additional Information
- Journal: Bull. Amer. Math. Soc. 77 (1971), 878-890
- MSC (1970): Primary 28A65; Secondary 54H20
- DOI: https://doi.org/10.1090/S0002-9904-1971-12803-3
- MathSciNet review: 0288233