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Suspensions of topological transformation groups

Published online by Cambridge University Press:  19 September 2008

David B. Ellis
David B. Ellis
Affiliation:
Beloit College Box 82, Beloit WI 53511, USA
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Abstract

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Let S be a subgroup of a topological group T, and suppose that S acts on a space X. One can form a T-transformation group (X ×sT, T) called the suspension of the S-transformation group (X, S). In this paper we study the relationship between the dynamical properties of (X, S) and those of its suspension when S is syndetic in T. The main tool used in this study is a notion of the group of a minimal flow (X, T) which is sensitive to the topology on the group T. We are able, using this group and the enveloping semigroup to obtain results on which T-transformation groups can be realized as suspensions of S-transformation groups, and give conditions under which the suspension of an equicontinuous S-flow is an equicontinuous T-flow.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 10 , Issue 1 , March 1990 , pp. 101 - 117
Copyright
Copyright © Cambridge University Press 1990

References

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