Hostname: page-component-7c8c6479df-5xszh Total loading time: 0 Render date: 2024-03-28T15:27:33.624Z Has data issue: false hasContentIssue false

Transitive flows: a semi-group approach

Published online by Cambridge University Press:  26 February 2010

J. D. Lawson
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.
Amha Lisan
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, U.S.A.
Get access

Abstract

In this paper we characterize the universal pointed actions of a semigroup S on a compact space such that the orbit of the distinguished point is dense; such actions are called transitive. The characterization is given in terms of the universal right topological monoidal compactification of S. All transitive actions are shown to arise as quotients modulo left congruences on this universal compactification. Minimal actions are considered, and close connections between these and minimal left ideals of the compactification are derived.

MSC classification

Type
Research Article
Copyright
Copyright © University College London 1991

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Auslander, J.. Minimal Flows and their Extensions (North-Holland, Amsterdam, 1988).Google Scholar
2.Berglund, J. E., Junghenn, H. D. and Milnes, P.. Analysis on Semigroups (John Wiley & Sons, New York, 1989).Google Scholar
3.Carruth, J. H., Hildebrant, J. A. and Koch, R. J.. The Theory of Topological Semigroups (Marcel Dekker, New York, 1983).Google Scholar
4.Devaney, R. L.. Chaotic Dynamical Systems, Second Edition (Addison-Wesley, New York, 1989).Google Scholar
5.Ellis, R.. Lectures on Topological Dynamics (Benjamin, New York, 1969).Google Scholar
6.Glasner, S.. Proximal Flows, Springer Lecture Notes in Mathematics 517 (Springer-Verlag, Heidelberg, 1976).CrossRefGoogle Scholar
7.Gottschalk, W. H.. Almost periodic points with respect to transformation semi-groups. Annals of Math., 47 (1946), 762766.CrossRefGoogle Scholar
8.Lawson, J. D.. Points of continuity for semigroup actions. Trans. Am. Math. Soc, 284 (1984), 183202.CrossRefGoogle Scholar
9.Ruppert, W. A. F.. Endomorphic actions of β(N) on the torus group. Semigroup Forum, 43 (1991), 202217.CrossRefGoogle Scholar