Hostname: page-component-cb9f654ff-pvkqz Total loading time: 0 Render date: 2025-09-05T08:44:24.010Z Has data issue: false hasContentIssue false
  • English
  • Français

A topological version of a theorem of Veech and almost simple flows

Published online by Cambridge University Press:  19 September 2008

Eli Glasner
Eli Glasner
Affiliation:
School of Mathematical Sciences, The Raymond and Beverly Sackler Faculty of Exact Sciences, 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.

Almost simple (AS) minimal flows are defined and it is shown that any factor map of an AS flow is, up to almost 1−1 equivalence, a group factor. An analogous theorem for metric, regular, point distal extensions is proved. In particular a theorem of Gottschalk is strengthened to show that any regular, point distal, metric flow is equicontinuous. When the acting group T is commutative it is shown that every proper minimal joining of an AS flow X and a minimal flow Y, is, up to almost 1−1 extensions, the relative product of X and Y over a common factor which is a group factor of X.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 3 , September 1990 , pp. 463 - 482
Copyright
Copyright © Cambridge University Press 1990

References

REFERENCES

[A]Auslander, J.. Endomorphisms of minimal sets. Duke Math. J. 30 (1963), 605–614.CrossRefGoogle Scholar
[A1]Auslander, J.. Minimal Flows and Their Extensions. Math. Studies 153, North-Holland: Amsterdam, 1988.Google Scholar
[B]Bronšteǐn, I. U.. Extensions of Minimal Transformation Groups. Sijthoff & Noordhoff: 1979.CrossRefGoogle Scholar
[E1]Ellis, R.. Lectures on Topological Dynamics. Benjamin: New York, 1969.Google Scholar
[E2]Ellis, R.. The Veech structure theorem. Trans. Amer. Math. Soc. 186 (1973), 203–218.CrossRefGoogle Scholar
[E-G]Ellis, R. & Glasner, S.. Pure weak mixing. Trans. Amer. Math. Soc. 243 (1978), 135–146.CrossRefGoogle Scholar
[G1]Glasner, S.. Proximal flows. Lecture Notes in Math. 517. Springer Verlag: New York, 1976.CrossRefGoogle Scholar
[G-W]Glasner, S. & Weiss, B.. A weakly mixing upside down tower of isometric extensions. Ergod. Th. & Dynam. Sys. 1 (1981), 151–157.CrossRefGoogle Scholar
[Go]Gottschalk, W. H.. Transitivity and equicontinuity. Bull. Amer. Math. Soc. 54 (1948), 982–984.CrossRefGoogle Scholar
[J]Junco, A. delOn minimal self-joinings in topological dynamics. Ergod. Th. & Dynam. Sys. 7 (1987), 211–227.CrossRefGoogle Scholar
[J-R]del Junco, A. & Rudolph, D.. On ergodic actions whose self-joinings are graphs. Ergod. Th. & Dynam. Sys. 7 (1987), 531–557.CrossRefGoogle Scholar
[V1]Veech, W. A.. Topological Dynamics, Bull. Amer. Math. Soc. 83 (1977), 775–830.CrossRefGoogle Scholar
[V2]Veech, W. A.. A criterion for a process to be prime. Monat. Math. 94 (1982), 335–341.CrossRefGoogle Scholar
[V3]Veech, W. A.. Point-distal flows. Amer. J. Math. 92 (1970), 205–242.CrossRefGoogle Scholar