Dynamical simplices and minimal homeomorphisms
Dynamical Systems
2016-11-08 v2 Logic
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.
Cite
@article{arxiv.1511.09280,
title = {Dynamical simplices and minimal homeomorphisms},
author = {Tomás Ibarlucía and Julien Melleray},
journal= {arXiv preprint arXiv:1511.09280},
year = {2016}
}