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Unique ergodicity of the automorphism group of the semigeneric directed graph. (English) Zbl 1505.37017

Let \(\mathbb{S}\) denote the semigeneric directed graph in the sense of G. L. Cherlin’s classification [Mem. Am. Math. Soc. 621, 161p. (1998; Zbl 0978.03029)]. It is proved that the automorphism group \(\mathrm{Aut}(\mathbb{S})\) is uniquely ergodic, that is, every minimal flow admits a unique Borel probability measure that is invariant under the action of the group.

MSC:

37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
37A25 Ergodicity, mixing, rates of mixing
37E25 Dynamical systems involving maps of trees and graphs
22F50 Groups as automorphisms of other structures
03C15 Model theory of denumerable and separable structures
43A07 Means on groups, semigroups, etc.; amenable groups

Citations:

Zbl 0978.03029
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References:

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