Real cocycles of point-distal minimal flows

Gernot Greschonig

doi:10.3934/proc.2015.0540

Article Contents

2015, Volume 2015: 540-548. Doi: 10.3934/proc.2015.0540 open access

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Real cocycles of point-distal minimal flows

Gernot Greschonig^1,

1.
Institute of Discrete Mathematics and Geometry, Vienna University of Technology (TU Vienna), Wiedner Hauptstraße 8-10, A1040 Vienna

Received: June 30, 2014

Revised: May 31, 2015

Published: October 2015

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Abstract

We generalise the structure theorem for topologically recurrent real skew product extensions of distal minimal compact metric flows in [9] to a class of point distal minimal compact metric flows. While the general case of a point distal flow according to the Veech structure theorem seems hopeless, we prove a result for cocycles of minimal point distal flows without strong Li-Yorke pairs which can be obtained by an almost 1-1 extension of a distal flow with connected fibres. Moreover, a stronger condition on recurrence is necessary. We shall assume that every non-distal point in the point distal compact metric flow is proximal to a point which lifts to recurrent points in the skew product. However, we shall prove that the usual notion of topological recurrence is sufficient for locally connected almost 1-1 extensions of an isometry. This setting includes a well-known example of a point-distal flow by Mary Rees.

Keywords:

Topological cocycles,
point-distal minimal homeomorphisms.

Mathematics Subject Classification: Primary: 37B05, 37B20, 54H20.

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References

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