TY - JOUR

T1 - The structure of tame minimal dynamical systems

AU - Glasner, Eli

PY - 2007/12

Y1 - 2007/12

N2 - A dynamical version of the Bourgain-Fremlin-Talagrand dichotomy shows that the enveloping semigroup of a dynamical system is either very large and contains a topological copy of βℕ, or it is a 'tame' topological space whose topology is determined by the convergence of sequences. In the latter case, the dynamical system is said to be tame. We use the structure theory of minimal dynamical systems to show that, when the acting group is Abelian, a tame metric minimal dynamical system (i) is almost automorphic (i.e. it is an almost one-to-one extension of an equicontinuous system), and (ii) admits a unique invariant probability measure such that the corresponding measure-preserving system is measure-theoretically isomorphic to the Haar measure system on the maximal equicontinuous factor.

AB - A dynamical version of the Bourgain-Fremlin-Talagrand dichotomy shows that the enveloping semigroup of a dynamical system is either very large and contains a topological copy of βℕ, or it is a 'tame' topological space whose topology is determined by the convergence of sequences. In the latter case, the dynamical system is said to be tame. We use the structure theory of minimal dynamical systems to show that, when the acting group is Abelian, a tame metric minimal dynamical system (i) is almost automorphic (i.e. it is an almost one-to-one extension of an equicontinuous system), and (ii) admits a unique invariant probability measure such that the corresponding measure-preserving system is measure-theoretically isomorphic to the Haar measure system on the maximal equicontinuous factor.

UR - http://www.scopus.com/inward/record.url?scp=36248970529&partnerID=8YFLogxK

U2 - 10.1017/S0143385707000296

DO - 10.1017/S0143385707000296

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AN - SCOPUS:36248970529

SN - 0143-3857

VL - 27

SP - 1819

EP - 1837

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 6

ER -