منابع مشابه
Uniformly Recurrent Subgroups
We define the notion of uniformly recurrent subgroup, URS in short, which is a topological analog of the notion of invariant random subgroup (IRS), introduced in [2]. Our main results are as follows. (i) It was shown in [26] that for an arbitrary countable infinite group G, any free ergodic probability measure preserving G-system admits a minimal model. In contrast we show here, using URS’s, th...
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10.2. Example We consider the abstract dynamical system given in 9.18: the shift system over S where the phase space X is the product space {1, . . . , r}, for some r ≥ 2. For any R ⊆ S, there are x and U such that R(x, U) = R: simply pick x ∈ X be such that x(s) = 1 iff s ∈ R; so x might be considered as a characteristic function of R. Put U = {z ∈ X : z(1S) = 1}, a clopen subset of X. Then fo...
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2018
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2018.47