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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
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Abstract

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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.

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

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