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Realizing uniformly recurrent subgroups

Published online by Cambridge University Press:  10 July 2018

NICOLÁS MATTE BON  and
TODOR TSANKOV
NICOLÁS MATTE BON
Affiliation:
D-MATH – ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland email nicolas.matte@math.ethz.ch
TODOR TSANKOV
Affiliation:
Institut de Mathématiques de Jussieu–PRG, Université Paris Diderot, 75205 Paris cedex 13, France Département de Mathématiques et Applications, École Normale Supérieure, 75005 Paris, France email todor@math.univ-paris-diderot.fr
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Abstract

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.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 2 , February 2020 , pp. 478 - 489
Copyright
© Cambridge University Press, 2018 

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