# American Institute of Mathematical Sciences

2015, 2015(special): 540-548. doi: 10.3934/proc.2015.0540

## Real cocycles of point-distal minimal flows

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

Received  July 2014 Revised  June 2015 Published  November 2015

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.
Citation: Gernot Greschonig. Real cocycles of point-distal minimal flows. Conference Publications, 2015, 2015 (special) : 540-548. doi: 10.3934/proc.2015.0540
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##### References:
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