Dynamical simplices and minimal homeomorphisms

Ibarlucía, Tomás; Melleray, Julien

doi:10.1090/proc/13578

Dynamical simplices and minimal homeomorphisms
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by Tomás Ibarlucía and Julien Melleray PDF

Proc. Amer. Math. Soc. 145 (2017), 4981-4994 Request permission

Abstract:

We give a characterization of sets $K$ of probability measures on a Cantor space $X$ with the property that there exists a minimal homeomorphism $g$ of $X$ such that the set of $g$-invariant probability measures on $X$ coincides with $K$. This extends theorems of Akin (corresponding to the case when $K$ is a singleton) and Dahl (when $K$ is finite-dimensional). Our argument is elementary and different from both Akin’s and Dahl’s.

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