Non-homogeneous extensions of Cantor minimal systems

Deeley, Robin; Putnam, Ian; Strung, Karen

doi:10.1090/proc/15342

Non-homogeneous extensions of Cantor minimal systems
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by Robin J. Deeley, Ian F. Putnam and Karen R. Strung PDF

Proc. Amer. Math. Soc. 149 (2021), 2081-2089 Request permission

Abstract:

Floyd gave an example of a minimal dynamical system which was an extension of an odometer and the fibres of the associated factor map were either singletons or intervals. Gjerde and Johansen showed that the odometer could be replaced by any Cantor minimal system. Here, we show further that the intervals can be generalized to cubes of arbitrary dimension and to attractors of certain iterated function systems. We discuss applications.

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