Almost topological dynamical systems. (English) Zbl 0441.28008


28D05 Measure-preserving transformations
54H20 Topological dynamics (MSC2010)
28D10 One-parameter continuous families of measure-preserving transformations


Zbl 0405.28017
Full Text: DOI


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.