Inventiones mathematicae

, Volume 111, Issue 1, pp 69–76

Mixing automorphisms of compact groups and a theorem of Schlickewei

  • Klaus Schmidt
  • Tom Ward
Article

Summary

We prove that every mixing ℤd by automorphisms of a compact, connected, abelian group is mixing of all orders.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AM] Atiyah, M., MacDonald, I.G.: Introduction to Commutative Algebra. Reading, MA: Addison-Wesley 1969Google Scholar
  2. [KS1] Kitchens, B., Schmidt, K.: Automorphisms of compact groups. Ergodic Theory Dyn. Sys.9, 691–735 (1989)Google Scholar
  3. [KS2] Kitchens, B., Schmidt, K.: Mixing Sets and Relative Entropies for Higher Dimensional Markov Shifts. (Preprint 1991)Google Scholar
  4. [La] Lang, S.: Algebra, 2nd ed. Reading, MA: Addison-Wesley 1984Google Scholar
  5. [Le] Ledrappier, F.: Un champ markovien peut être d'entropie nulle et mélangeant. C.R. Acad. Sci. Paris, Ser.A 287, 561–562 (1978)Google Scholar
  6. [Li] Lind, D.: The structure of skew products with ergodic group automorphisms. Isr. J. Math.28, 205–248 (1977)Google Scholar
  7. [LSW] Lind, D., Schmidt, K., Ward, T.: Mahler measure and entropy for commuting automorphisms of compact groups. Invent. Math.101, 593–629 (1990)Google Scholar
  8. [MT] Miles, G., Thomas, R.K.: The breakdown of automorphisms of compact topological groups. In: Studies in Probability and Ergodic Theory. (Adv. Math. Suppl. Stud., vol. 2, pp. 207–218) New York London: Academic Press 1987Google Scholar
  9. [S] Schlickewei, H.P.:S-unit equations over number fields. Invent. Math.102, 95–107 (1990)Google Scholar
  10. [Sc1] Schmidt, K.: Automorphisms of compact abelian groups and affine varieties. Proc. Lond. Math. Soc.61, 480–496 (1990)Google Scholar
  11. [Sc2] Schmidt, K.: Mixing automorphisms of compact groups and a theorem by Kurt Mahler. Pac. J. Math.137, 371–384 (1989)Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Klaus Schmidt
    • 1
  • Tom Ward
    • 2
  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK
  2. 2.Department of MathematicsOhio State UniversityColumbusUSA

Personalised recommendations