Faces of simplices of invariant measures for actions of amenable groups

2016/03/09 by Bartosz Frej, Frej, Bartosz, Dawid Huczek +1
Mathematics · #37A15 #37B05 #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DS #msc:37A15 #msc:37B05

paper · pdf · doi:10.48550/arxiv.1603.03018

arxiv created 2016/03/09 · openalex publication_date 2016/03/09 · arxiv updated 2016/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every face in the simplex of invariant measures on a zero-dimensional dynamical system with free action of an amenable group G can be modeled as the entire simplex of invariant measures on some other zero-dimensional dynamical system with free action of G.

Citations

• Minimal models for actions of amenable groups

Related

• Zero-dimensional extensions of amenable group actions
• Minimal models for actions of amenable groups
• Mean dimension and a non-embeddable example for amenable group actions
• Invariant measures for actions of congruent monotileable amenable groups
• Invariant measures in simple and in small theories