Mathematical systems theory

, Volume 1, Issue 1, pp 1–49 | Cite as

Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation

  • Harry Furstenberg


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Adler, R. L., Konheim, A. G. andMcAndrew, M. H., Topological entropy,Trans. Amer. Math. Soc. 114 (1965), 309–319.Google Scholar
  2. [2]
    Ellis, R., Distal transformation groups,Pacific J. Math. 8 (1958), 401–405.Google Scholar
  3. [3]
    Furstenberg, H.,Stationary Processes and Prediction Theory Princeton Univ. Press, Princeton, 1960.Google Scholar
  4. [4]
    Furstenberg, H., Strict ergodicity and transformations of the torus,Amer. J. Math. 83 (1961), 573–601.Google Scholar
  5. [5]
    Furstenberg, H., The structure of distal flows,Amer. J. Math. 85 (1963), 477–515.Google Scholar
  6. [6]
    Gottschalk, W. H., andHedlund, G. A.,Topological Dynamics, Amer. Math. Soc. Colloq. Publ., Vol. 83, 1961.Google Scholar
  7. [7]
    Gottschalk, W. H., An irreversible minimal set, inErgodic Theory Academic Press, New York, 1963.Google Scholar
  8. [8]
    Halmos, P. R., On automorphisms of compact groups,Bull. Amer. Math. Soc. 49 (1943), 619–624.Google Scholar
  9. [9]
    Halmos, P. R.,Lectures on Ergodic Theory Publ. Math. Soc. Japan, Tokyo, 1956.Google Scholar
  10. [10]
    Halmos, P. R.,Entropy in Ergodic Theory Univ. Chicago Press, Chicago, 1959.Google Scholar
  11. [11]
    Niven, I., andZuckerman, H. S., On the definition of normal number,Pacific J. Math. 1 (1951), 103–109.Google Scholar
  12. [12]
    Robbins, H. E., On a class of recurrent sequences,Bull. Amer. Math. Soc. 43 (1937), 413–417.Google Scholar
  13. [13]
    Rokhlin, V. A., New progress in the theory of transformations with invariant measure,Russian Math. Surveys 15 (1960), 1–22.Google Scholar
  14. [14]
    Wu, T. S., On homomorphisms in topological dynamics, (to appear).Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1967

Authors and Affiliations

  • Harry Furstenberg
    • 1
  1. 1.The Hebrew UniversityJerusalemIsrael

Personalised recommendations