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Minimal flows of finite almost periodic rank

Published online by Cambridge University Press:  19 September 2008

Joseph Auslander  and
Nelson Markley
Joseph Auslander
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA
Nelson Markley
Affiliation:
Department of Mathematics, University of Maryland, College Park, Maryland 20742, USA
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Abstract

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The totally minimal flow (X, T) is said to have finite almost periodic rank if there is a positive integer n such that whenever (x1, x2,…, xn+1) is an almost periodic point of the product flow (Xn+1, T×…×T) then, for some i≠j, xi, and xj are in the same orbit. The rank of (X, T) is the smallest such integer. If (Y, S) is a graphic flow, (Y, Sn) has rank |n| and it is shown that every finite rank flow has, modulo a proximal extension, a graphic power factor. Various classes of finite rank flows are defined, and characterized in terms of their Ellis groups. There are four disjoint types which have basic structural differences.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Issue 2 , June 1988 , pp. 155 - 172
Copyright
Copyright © Cambridge University Press 1988

References

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