Ergodic Properties of Tame Dynamical Systems

Ergodic Properties of Tame Dynamical Systems

The problem of the *-weak decomposability into ergodic components of a topological ℕ 0 -dynamical system (Ω, φ), where φ is a continuous endomorphism of a compact metric space Ω, is considered in terms of the associated enveloping semigroups. It is shown that, in the tame case (where the Ellis semig...

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Veröffentlicht in:Mathematical Notes 2019-07, Vol.106 (1-2), p.286-295
1. Verfasser: Romanov, A. V.
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Decomposition
Dynamical systems
Ergodic processes
Mathematics
Mathematics and Statistics
Metric space
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description The problem of the *-weak decomposability into ergodic components of a topological ℕ 0 -dynamical system (Ω, φ), where φ is a continuous endomorphism of a compact metric space Ω, is considered in terms of the associated enveloping semigroups. It is shown that, in the tame case (where the Ellis semigroup E (Ω, φ) consists of endomorphisms of Ω of the first Baire class), such a decomposition exists for an appropriately chosen generalized sequential averaging method. A relationship between the statistical properties of (Ω, φ) and the mutual structure of minimal sets and ergodic measures is discussed.
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subjects Decomposition
Dynamical systems
Ergodic processes
Mathematics
Mathematics and Statistics
Metric space
title Ergodic Properties of Tame Dynamical Systems
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