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Non-homogeneous extensions of Cantor minimal systems


Authors: Robin J. Deeley, Ian F. Putnam and Karen R. Strung
Journal: Proc. Amer. Math. Soc. 149 (2021), 2081-2089
MSC (2020): Primary 37B05, 46L35, 46L85, 19K99
DOI: https://doi.org/10.1090/proc/15342
Published electronically: February 24, 2021
MathSciNet review: 4232200
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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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Additional Information

Robin J. Deeley
Affiliation: Department of Mathematics, University of Colorado Boulder Campus Box 395, Boulder, Colorado 80309-0395
MR Author ID: 741108
Email: robin.deeley@gmail.com

Ian F. Putnam
Affiliation: Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
MR Author ID: 142845
Email: ifputnam@uvic.ca

Karen R. Strung
Affiliation: Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Prague, Czech Republic
MR Author ID: 924942
Email: strung@math.cas.cz

Keywords: Minimal dynamics
Received by editor(s): July 18, 2019
Received by editor(s) in revised form: August 28, 2020, and September 15, 2020
Published electronically: February 24, 2021
Additional Notes: The first author was funded by NSF Grant DMS 2000057 and by Simons Foundation Collaboration Grant for Mathematicians number 638449.
The second author was supported in part by an NSERC Discovery Grant.
The third author was funded by GAČR project 20-17488Y and RVO: 67985840 and part of this work was carried out while funded by Sonata 9 NCN grant 2015/17/D/ST1/02529 and a Radboud Excellence Initiative Postdoctoral Fellowship.
Communicated by: Nimish Shah
Article copyright: © Copyright 2021 American Mathematical Society