Geodesic
Ergodic Properties of Tame Dynamical Systems
Matematičeskie zametki, Tome 106 (2019) no. 2, pp. 295-306

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The problem of the $*$-weak decomposability into ergodic components of a topological $\mathbb N_0$-dynamical system $(\Omega,\varphi)$, where $\varphi$ is a continuous endomorphism of a compact metric space $\Omega$, is considered in terms of the associated enveloping semigroups. It is shown that, in the tame case (where the Ellis semigroup $E(\Omega,\varphi)$ consists of endomorphisms of $\Omega$ of the first Baire class), such a decomposition exists for an appropriately chosen generalized sequential averaging method. A relationship between the statistical properties of $(\Omega,\varphi)$ and the mutual structure of minimal sets and ergodic measures is discussed.
Keywords: ergodic mean, tame dynamical system, enveloping semigroup. 
@article{MZM_2019_106_2_a10,
     author = {A. V. Romanov},
     title = {Ergodic {Properties} of {Tame} {Dynamical} {Systems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {295--306},
     publisher = {mathdoc},
     volume = {106},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_106_2_a10/}
}
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A. V. Romanov. Ergodic Properties of Tame Dynamical Systems. Matematičeskie zametki, Tome 106 (2019) no. 2, pp. 295-306. http://geodesic.mathdoc.fr/item/MZM_2019_106_2_a10/