Minimal skew products

Glasner, S.

doi:10.1090/S0002-9947-1980-0574795-2

Minimal skew products
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Trans. Amer. Math. Soc. 260 (1980), 509-514 Request permission

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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