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Article Dans Une Revue Ergodic Theory and Dynamical Systems Année : 2020

Realizing uniformly recurrent subgroups

Résumé

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.
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Dates et versions

hal-04152219 , version 1 (10-07-2024)

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Nicolás Matte Bon, Todor Tsankov. Realizing uniformly recurrent subgroups. Ergodic Theory and Dynamical Systems, 2020, 40 (2), pp.478-489. ⟨10.1017/etds.2018.47⟩. ⟨hal-04152219⟩
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