Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-28T03:18:02.566Z Has data issue: false hasContentIssue false
  • English
  • Français

Topological dynamics and ergodic theory

Published online by Cambridge University Press:  19 September 2008

Robert Ellis
Robert Ellis
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that when viewed properly some concepts in topological dynamics and ergodic theory are not merely analogous but equivalent. Also the Mackey-Halmos-von Neumann theorem on ergodic processes with discrete spectrum is generalized and an account of the Mackey-Zimmer theory of minimal cocycles is given in a more general setting.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 7 , Issue 1 , March 1987 , pp. 25 - 47
Copyright
Copyright © Cambridge University Press 1987

References

REFERENCES

[1]Bourbaki, N.. Intégration. Hermann, Paris, 1965.Google Scholar
[2]Dixmier, J.. Sur certains espaces considéréd par. M. H. Stone. Summa Brasil, Math. t.2. fasc. 11 (1951), 151–182.Google Scholar
[3]Ellis, R.. Locally compact transformation groups. Duke Math. Journal, 24 (1957), 119–125.Google Scholar
[4]Ellis, R.. Lectures on Topological Dynamics. Benjamin, New York, 1969.Google Scholar
[5]Ellis, R.. The Furstenberg structure theorem. Pac. J. Math. 76 (1978), 345–349.Google Scholar
[6]Gleason, A. M.. Projective topological spaces, Ill. J. Math. 2 (1958), 482–489.Google Scholar
[7]Hofmann, K. H. & Keimel, K.. Bundles and sheaves of Banach spaces, C(X)-modules. Lec. Notes in Math. 753 (Berlin, Springer-Verlag) (1979), 415–441.Google Scholar
[8]Keynes, H. B. & Newton, D.. The structure of ergodic measures for compact group extensions. Israel J. of Math., 18 (1974), 363–399.CrossRefGoogle Scholar
[9]Mackey, G. W.. Point realizations of transformation groups. Ill. J. Math., 6 (1962), 327–335.Google Scholar
[10]Zimmer, R. J.. Extensions of ergodic group actions. Ill. J. Math. 20 (1976), 373–409.Google Scholar