Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T13:34:27.821Z Has data issue: false hasContentIssue false
  • English
  • Français

Iterated extensions

Published online by Cambridge University Press:  13 August 2009

Robert Ellis  and
Shmuel Glasner
Robert Ellis
Affiliation:
Minnesota 55455, and Department of Mathematics, Tel Aviv University, Tel Aviv, Israel
Shmuel Glasner
Affiliation:
Minnesota 55455, and Department of Mathematics, Tel Aviv University, Tel Aviv, Israel
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.

The notion of an iterated extension of a flow is introduced and studied. In particular it is shown how eigenfunctions occur in a natural way. This is then exploited to produce an example of a weakly mixing minimal set with a non-weakly mixing quasi-factor.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 2 , Issue 1 , March 1982 , pp. 1 - 13
Copyright
Copyright © Cambridge University Press 1982

References

REFERENCES

[1]Ellis, R.. Lectures in Topological Dynamics. Benjamin: New York, 1969.Google Scholar
[2]Ellis, R.. Cocycles in topological dynamics. Topology 17 (1978), 111–130.CrossRefGoogle Scholar
[3]Ellis, R.. The Veech structure theorem, Trans. Amer. Math. Soc. 186 (1973), 203–218.CrossRefGoogle Scholar
[4]Ellis, R. & Glasner, S.. Pure weak mixing. Trans. Amer. Math. Soc. 243 (1978), 135–146CrossRefGoogle Scholar
[5]Ellis, R.. Glasner, S. & Shapiro, L.. Algebraic equivalents of flow disjointness. Illinois J. Math. 20 (1976), 354–360.CrossRefGoogle Scholar
[6]Peleg, R.. Some extensions of weakly mixing flows. Israel J. Math. 9 (1971), 330–336.CrossRefGoogle Scholar
[7]Rees, M.. On the structure of minimal distal transformation groups with topological manifolds as phase spaces, Maths. Inst. Univ. of Warwick, Coventry (1977).Google Scholar