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ℤn and ℝn cocycle extensions and complementary algebras

Published online by Cambridge University Press:  19 September 2008

Daniel J. Rudolph
Daniel J. Rudolph
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA
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Abstract

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We present here an investigation of the degree to which mixing properties can be shown to lift to cocycle extensions of an ergodic map by ℤn and ℝn weakly mixing actions. A number of other results on such extensions are also included.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 4 , December 1986 , pp. 583 - 599
Copyright
Copyright © Cambridge University Press 1986

References

REFERENCES

[A-Kat]Anosov, D. V. & Katok, A. B.. New examples in smooth ergodic theory. Trans. Moscow Math. Soc. 23 (1970), 1–35.Google Scholar
[dJ-R]Junco, A. del & Rudolph, D. J.. Kakutani equivalence of ergodic ℤn actions. Ergod. Th. & Dynam. Sys. (to appear).Google Scholar
[F]Furstenberg, H.. Disjointness in ergodic theory, minimal sets and a problem in diophantine approximation. Math. Syst. Theory 1 (1967), 1–49.Google Scholar
[F-W]Furstenberg, H. & Weiss, B.. The finite multipliers of infinite ergodic transformations. In Springer Lecture Notes in Maths. 668, Structure of Attractors, (1977).Google Scholar
[Kal]Kalikow, S.. The T, T−1 transformation is not loosely Bernoulli. Preprint.Google Scholar
[Kat]Katok, A. B.. Smooth non-Bernoulli K-automorphisms. Inv. Math. 61 (1980), 291–300.CrossRefGoogle Scholar
[Ko]Kočergin, A. V.. Time changes in flows and mixing. Math. USSR Izvestija 7 (1973), No. 6, 1273–1294.Google Scholar
[M]Meilijson, I.. Mixing properties of a class of skew products. Israel J. Math. 19 (1974), 266–270.CrossRefGoogle Scholar
[R1]Rudolph, D. J.. Classifying the isometric extensions of a Bernoulli shift. J. d'anal. Math. 34 (1978), 36–60.Google Scholar
[R2]Rudolph, D. J., k-fold mixing lifts to weakly mixing isometric extensions. Preprint.CrossRefGoogle Scholar
[R3]Rudolph, D. J.. Inner and barely linear time changes of ergodic ℝk actions. Com. Math. 26 (1984), 351–369.Google Scholar
[PI]Parry, W.. Ergodic properties of affine transformations and flows on nilmanifolds. Amer. J. of Math. 91 (1969), 757–771.Google Scholar
[P2]Parry, W.. Cocycles and velocity changes. J. London Math Soc. 5 (1972), 511–516.CrossRefGoogle Scholar