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| In this talk we generalise results on the structure of real-valued cocycles of distal minimal compact metric flows for cocycles of a class of point-distal minimal flows (i.e. minimal flows with at least one point distal to any distinct point, which is sufficient for a residual set of points with this property).
Since the general case of a point-distal minimal flow according to the Veech structure theorem seems illusive, we will consider minimal compact metric flows without strong Li-Yorke pairs (i.e. proximal pairs recurrent in the product space) which are almost 1-1 extensions of a distal flow with connected fibres.
For this class of flows, which includes the point-distal flows on the torus constructed by Mary Rees, we can understand the structure of real-valued cocycles under a condition on recurrent points in the skew product of the cocycle.
This condition requires that every non-distal point in the point-distal minimal compact flow is proximal to a point which lifts to recurrent points in the skew product. |
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