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Working paper

Ergodic Properties of tame dynamical systems

arxiv.org. math. Cornell University, 2018. No. 1806.09132.
We study the problem on the weak-star decomposability of a topological N0-dynamical system (Ω, '), where ' 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,') 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 ◦ ', x ∈ C(Ω), contains a pointwise convergent subsequence. We also discuss the relationship between the statistical properties of (Ω, ') and the mutual structure of minimal sets and ergodic measures.