Advertisement

Israel Journal of Mathematics

, Volume 19, Issue 3, pp 228–236 | Cite as

Skew products of Bernoulli shifts with rotations. II

  • R. L. Adler
  • P. C. Shields
Article

Abstract

IfT is a weakly mixing skew product transformation defined byT(x, y)x, y+f(x) (mod 1)), where σ is a Bernoulli shift andf is a function satisfying a Hölder type condition and measurable with respect to the past of an independent partition of σ, thenT is Bernoulli.

Keywords

Lebesgue Space Geodesic Flow Bernoulli Shift Measure Preserve Transformation Horizontal Fiber 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. L. Adler and P. C. Shields,Skew products of Bernoulli shifts with rotations, Israel J. Math.12 (1972), 215–222.zbMATHMathSciNetGoogle Scholar
  2. 2.
    H. Anzai,Ergodic Skew product transformations on the torus, Osaka J. Math.3 (1951), 83–99.zbMATHMathSciNetGoogle Scholar
  3. 3.
    P. R. Halmos,Lectures on Ergodic Theory, Chelsea Publishing Co., New York (1956).zbMATHGoogle Scholar
  4. 4.
    D. S. Ornstein,Imbedding Bernoulli Shifts in flows, Contributions to ergodic theory and probability, Lecture Notes in Math., Springer Berlin (1970), 178–218.Google Scholar
  5. 5.
    D. Ornstein,Two Bernoulli shifts with infinite entropy are isomorphic, Advances in Math.5 (1970), 339–348.CrossRefMathSciNetGoogle Scholar
  6. 6.
    D. Ornstein and B. Weiss,Geodesic flows are Bernoullian, Israel J. Math.14 (1973), 184–198.zbMATHMathSciNetGoogle Scholar
  7. 7.
    W. Parry,Ergodic properties of affine transformations and flows on nilmanifolds, Amer. J. Math.91 (1969), 757–771.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    V. A. Rokhlin and Ya G. Sinai,Construction and properties of invariant measurable partitions, Dokl. Akad. Nauk USSR141 (1961), 1038–1041.Google Scholar
  9. 9.
    P. Shields,The theory of Bernoulli shifts, Chicago lectures in Math. series, University of Chicago Press, Chicago (1973).zbMATHGoogle Scholar

Copyright information

© Hebrew University 1975

Authors and Affiliations

  • R. L. Adler
    • 1
  • P. C. Shields
    • 1
  1. 1.IBM Thomas J. Watson Research CenterYorktown HeightsU.S.A.

Personalised recommendations