2006/09/18 by Eli Glasner, Glasner, Eli · 2 citations
Computer Science · Mathematics · #46B20 #54H20 #Computability, Logic, AI Algorithms #FOS: Mathematics #Functional Analysis (math.FA) #General Mathematics (math.GM) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.math/0609503
openalex publication_date 2006/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 β\N, or it is a "tame" topological space whose topology is determined by the convergence of sequences. In the latter case the dynamical system is called 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 1-1 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.