Topologically mixing and minimal but not ergodic, analytic transformation onT5

  • Bassam R. Fayad


We give an example of an analytic transformation onT5 that conserves the Haar measure, that is minimal and topologically mixing, but is not ergodic.


measure preserving minimal topologically mixing nonergodic time change reparametrization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    B. R. Fayad. Analytic mixing reparametrizations of irrational flows on the torusT n,n≥3.To appear in Ergodic Theory Dynamical Systems.Google Scholar
  2. [2]
    H. Furstenberg. Strict ergodicity and transformation of the torus.Amer. J. Math.,83: (1961), 573–601.Google Scholar
  3. [3]
    Anatole Katok and Boris Hasselblatt.Introduction to the modern theory of dynamical systems, chapter 4. Cambridge University Press, Cambridge, 1995.Google Scholar
  4. [4]
    J-C. Yoccoz.Petits diviseurs en dimension 1. Astérisque (1982), Appendix 1.Google Scholar
  5. [5]
    Zygmund.Trigonometric series, chapter VI, 6. Cambridge University Press, (1959).Google Scholar

Copyright information

© Sociedade Brasileira de Matemática 2000

Authors and Affiliations

  • Bassam R. Fayad
    • 1
  1. 1.Centre de Mathématiques UMR 7640 du CNRSÉcole PolytechniquePalaiseau CedexFrance

Personalised recommendations