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Almost topological dynamical systems. (English) Zbl 0441.28008

MSC:
28D05 Measure-preserving transformations
54H20 Topological dynamics (MSC2010)
28D10 One-parameter continuous families of measure-preserving transformations
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[1] R. Adler and B. Marcus,Finitistic coding for shifts of finite type, NSF Regional Conference North Dakota State Univ., to appear in Lecture Notes in Math., Springer Verlag.
[2] R. Adler and B. Weiss,Entropy, a complete invariant for automorphisms of the torus, Proc. Nat. Acad. Sci. U.S.A.57 (1967), 1573–1576. · Zbl 0177.08002
[3] M. A. Akcoglu, A. del Junco and M. Rahe,Finitary codes between Markov processes, submitted to Z. Wahrscheinlichkeitstheorie und Verw. Gebiete. · Zbl 0403.28017
[4] J. Blum and D. Hanson,On the isomorphism problem for Bernoulli schemes, Bull. Amer. Math. Soc.69 (1963), 221–223. · Zbl 0121.13601
[5] W. Böge, K. Krickeberg and F. Papangelou,Über die dem Lebesgueschen Maß isomorphen topologischen Maßräume, Manuscripta Math.1 (1969), 59–77. · Zbl 0164.06101
[6] C. Boldrighini, M. Keane and F. Marchetti,Billiards in polygons, Ann. Probability6 (1978), 532–540. · Zbl 0377.28014
[7] R. Bowen,Markov partitions for axiom A diffeomorphisms, Amer. J. Math.92 (1970), 725–747. · Zbl 0208.25901
[8] R. Bowen,Smooth partitions of Anosov diffeomorphisms are weak Bernoulli, Israel J. Math.21 (1975), 95–100. · Zbl 0315.58020
[9] M. Denker, C. Grillenberger and K. Sigmund,Ergodic theory on compact spaces, Lecture Notes in Math.527, Springer Verlag, 1976. · Zbl 0328.28008
[10] M. Denker,Generators and almost topological isomorphisms, Conference on Dynamical Systems and Ergodic Theory, Warszawa, 1977; Astérisque49 (1977), 23–36.
[11] M. Denker,Almost topological representation theorems for dynamical systems, to appear in Monatsh. Math. (1979). · Zbl 0405.54033
[12] M. I. Gordin,The central limit theorem for stationary processes, Dokl. Akad. Nauk SSSR188, No. 4 (1969)= Soviet. Math. Dokl.10, No. 5 (1969), 1174–1176. · Zbl 0212.50005
[13] W. H. Gottschalk and G. Hedlund,Topological Dynamics, Amer. Math. Soc. Coll. Publ.36.
[14] C. Grillenberger and U. Krengel,On marginal distributions and isomorphisms of stationary processes, Math. Z.149 (1976), 131–154. · Zbl 0322.60035
[15] I. A. Ibragimov and Yu. V. Linnik,Independent and Stationary Sequences of Random Variables, Wolters-Noordhoff Publishing, Groningen, 1971. · Zbl 0219.60027
[16] R. I. Jewett,The prevalence of uniquely ergodic systems, J. Math. Mech.19 (1970), 717–729. · Zbl 0192.40601
[17] M. Keane,Bernoulli-Schemata und Isomorphie, Diplomarbeit Universität, Göttingen, 1965.
[18] M. Keane,Coding problems in ergodic theory, Proc. Int. Conf. on Math. Physics 1974, Camerino, Italy.
[19] M. Keane,Interval exchange transformations, Math. Z.141 (1975), 25–31. · Zbl 0288.28020
[20] M. Keane and M. Smorodinsky,A class of finitary codes, Israel J. Math.26 (1977), 352–371. · Zbl 0357.94012
[21] K. Krickeberg,Strong mixing properties of Markov chains with infinite invariant measure, Proc. Fifth Berkeley Symp. Math. Stat. and Probability 1965, Vol. II, Part 2, Univ. of California Press, 1967, pp. 431–446.
[22] W. Krieger,On entropy and generators of measure preserving transformations, Trans. Amer. Math. Soc.149 (1970), 453–464, Erratum168 (1972), 519. · Zbl 0204.07904
[23] W. Krieger,On unique ergodicity, Proc. of the Sixth Berkeley Symp. on Math. Stat. and Probability, Berkeley, Univ. of California Press, 1972, pp. 327–346. · Zbl 0262.28013
[24] D. Lind and J.-P. Thouvenot,Measure-preserving homeomorphisms of the torus represent all finite entropy ergodic transformations, Math. Systems Theory11 (1977/78), 275–282. · Zbl 0377.28011
[25] L. Meshalkin,A case of isomorphy of Bernoulli schemes, Dokl. Akad. Nauk SSSR128 (1959), 41–44.
[26] J. C. Oxtoby,Maß und Kategorie, Springer Verlag, 1971.
[27] W. Parry,A finitary classification of topological Markov chains and sofic systems, preprint. · Zbl 0352.60054
[28] P. Walters,Ergodic Theory–Introductory Lectures, Lecture Notes in Math.458, Springer Verlag, 1975. · Zbl 0299.28012
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