Minimal skew products

Source abstract

Let ( σ , Z ) (\sigma ,\,Z) be a metric minimal flow. Let Y be a compact metric space and let g \mathcal {g} be a pathwise connected group of homeomorphisms of Y . We consider a family of skew product flows on Z × Y = X Z\, \times \,Y\, = \,X and show that when ( g , Y ) (\mathcal {g},\,Y) is minimal most members of this family have the property of being disjoint from every minimal flow which is disjoint from ( σ , Z ) (\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.