Dynamical simplices and minimal homeomorphisms

Tomás Ibarlucía (1) , Julien Melleray (1)

1 ICJ - Institut Camille Jordan

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.

Domaines: Systèmes dynamiques [math.DS]; Logique [math.LO]

Tomás Ibarlucía, Julien Melleray. Dynamical simplices and minimal homeomorphisms. 2015. ⟨hal-01235610v1⟩