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A context in which finite or unique ergodicity is generic

Part of: Topological dynamics Ergodic theory

Published online by Cambridge University Press:  29 September 2020

ANDY Q. YINGST
ANDY Q. YINGST*
Affiliation:
University of South Carolina Lancaster, PO Box 889, Lancaster, SC29721, USA (e-mail: andy.yingst@gmail.com)
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Abstract

We show that for good measures, the set of homeomorphisms of Cantor space which preserve that measure and which have no invariant clopen sets contains a residual set of homeomorphisms which are uniquely ergodic. Additionally, we show that for refinable Bernoulli trial measures, the same set of homeomorphisms contains a residual set of homeomorphisms which admit only finitely many ergodic measures.

Keywords

group actionssmooth dynamicsgood measuresunique ergodicity

MSC classification

Primary: 37A05: Measure-preserving transformations
Secondary: 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 10 , October 2021 , pp. 3178 - 3200
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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