Dynamical simplices and minimal homeomorphisms. (English) Zbl 1373.54046

Let \(K\) be a simplex of probability measures on a Cantor space \(X\). The main result in this paper is as below.
Theorem. The following assertions are equivalent:
(i) There exists a minimal homeomorphism \(g\) whose set of invariant measures is \(K\)
(ii) \(K\) is a dynamic simplex.
Further aspects involving these notions are also discussed.


54H20 Topological dynamics (MSC2010)
37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)


Zbl 1078.37004
Full Text: DOI arXiv


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