This is a preview of subscription content, log in via an institution to check access.
Bibliography
Adler, R. L., Konheim, A. G. andMcAndrew, M. H., Topological entropy,Trans. Amer. Math. Soc. 114 (1965), 309–319.
Ellis, R., Distal transformation groups,Pacific J. Math. 8 (1958), 401–405.
Furstenberg, H.,Stationary Processes and Prediction Theory Princeton Univ. Press, Princeton, 1960.
Furstenberg, H., Strict ergodicity and transformations of the torus,Amer. J. Math. 83 (1961), 573–601.
Furstenberg, H., The structure of distal flows,Amer. J. Math. 85 (1963), 477–515.
Gottschalk, W. H., andHedlund, G. A.,Topological Dynamics, Amer. Math. Soc. Colloq. Publ., Vol. 83, 1961.
Gottschalk, W. H., An irreversible minimal set, inErgodic Theory Academic Press, New York, 1963.
Halmos, P. R., On automorphisms of compact groups,Bull. Amer. Math. Soc. 49 (1943), 619–624.
Halmos, P. R.,Lectures on Ergodic Theory Publ. Math. Soc. Japan, Tokyo, 1956.
Halmos, P. R.,Entropy in Ergodic Theory Univ. Chicago Press, Chicago, 1959.
Niven, I., andZuckerman, H. S., On the definition of normal number,Pacific J. Math. 1 (1951), 103–109.
Robbins, H. E., On a class of recurrent sequences,Bull. Amer. Math. Soc. 43 (1937), 413–417.
Rokhlin, V. A., New progress in the theory of transformations with invariant measure,Russian Math. Surveys 15 (1960), 1–22.
Wu, T. S., On homomorphisms in topological dynamics, (to appear).
Author information
Authors and Affiliations
Additional information
This research was sponsored in part by the Air Force Office of Scientific Research and by a grant from the Sloan Foundation.
Rights and permissions
About this article
Cite this article
Furstenberg, H. Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation. Math. Systems Theory 1, 1–49 (1967). https://doi.org/10.1007/BF01692494
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01692494