2018/06/24 by A. V. Romanov, Romanov, A. V. · 1 citation
Mathematics · #20M20 (Secondary) #37A30 #47A35 (Primary) #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1806.09132
openalex publication_date 2018/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the problem on the weak-star decomposability of a topological ℕ0-dynamical system (Ω,φ), where φ is an endomorphism of a metric compact set Ω, into ergodic components in terms of the associated enveloping semigroups. In the tame case (where the Ellis semigroup E(Ω,φ) consists of B1-transformations Ω→ Ω), we show that (i) the desired decomposition exists for an appropriate choice of the generalized sequential averaging method; (ii) every sequence of weighted ergodic means for the shift operator x→ x∘φ, x∈ C(Ω), contains a pointwise convergent subsequence. We also discuss the relationship between the statistical properties of (Ω,φ) and the mutual structure of minimal sets and ergodic measures.