On minimal actions of countable groups

Eli Glasner; Benjamin Weiss

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arXiv · 1801.03308

On minimal actions of countable groups

Eli Glasner·Benjamin Weiss

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Abstract

Our purpose here is to review some recent developments in the theory of dynamical systems whose common theme is a link between minimal dynamical systems, certain Ramsey type combinatorial properties, and the Lovasz local lemma (LLL). For a general countable group G the two classes of minimal systems we will deal with are (I) the minimal subsystems of the {\em subgroup system} (Sub(G), G), called URS's (uniformly recurrent subgroups), and (II) minimal {\em subshifts}; i.e. subsystems of the binary Bernoulli G-shift ({0, 1}^G, {\sig_g}_{g \in G}).

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Eli Glasner, Benjamin Weiss. 2018-01-10. On minimal actions of countable groups. https://arxiv.org/abs/1801.03308

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