Dynamical simplices and minimal homeomorphisms. (English) Zbl 1373.54046

Ibarlucía, Tomás; Melleray, Julien

Proc. Am. Math. Soc. 145, No. 11, 4981-4994 (2017).

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.

Reviewer: Mihai Turinici (Iaşi)

MSC:

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

Keywords:

Cantor space; minimal homeomorphism; invariant measure; Kakutani-Rokhlin partitions

Citations:

Zbl 1078.37004

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