On minimal actions of countable groups

2018/01/10 by Glasner, Eli, Weiss, Benjamin
#05D10 #20E99 #37A50 (Primary) #37B10 (Secondary) #54H20 #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1801.03308

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_{gg ∈ G}).

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