Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Minimal skew products


Author: S. Glasner
Journal: Trans. Amer. Math. Soc. 260 (1980), 509-514
MSC: Primary 54H20
MathSciNet review: 574795
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Abstract: Let $ (\sigma ,\,Z)$ be a metric minimal flow. Let Y be a compact metric space and let $ \mathcal{g}$ be a pathwise connected group of homeomorphisms of Y. We consider a family of skew product flows on $ Z\, \times \,Y\, = \,X$ and show that when $ (\mathcal{g},\,Y)$ is minimal most members of this family have the property of being disjoint from every minimal flow which is disjoint from $ (\sigma ,\,Z)$. From this and some further results about skew product flows we deduce the existence of a minimal metric flow which is disjoint from every weakly mixing minimal flow but is not PI.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0574795-2
Keywords: Minimal flow, weakly mixing, disjointness, PI
Article copyright: © Copyright 1980 American Mathematical Society