2017/02/23 by Bon, Nicolás Matte, Tsankov, Todor
#Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1702.07101
We show that every uniformly recurrent subgroup of a locally compact group is the family of stabilizers of a minimal action on a compact space. More generally, every closed invariant subset of the Chabauty space is the family of stabilizers of an action on a compact space on which the stabilizer map is continuous everywhere. This answers a question of Glasner and Weiss. We also introduce the notion of a universal minimal flow relative to a uniformly recurrent subgroup and prove its existence and uniqueness.