Geodesic
Ordinary Semicascades and Their Ergodic Properties
Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 2, pp. 92-96

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A relationship is considered between ergodic properties of a discrete dynamical system on a compact metric space $\Omega$ and characteristics of companion algebro-topological objects, namely, the Ellis enveloping semigroup $E$, the Köhler enveloping operator semigroup $\Gamma$, and the semigroup $G$ being the closure of the convex hull of $\Gamma$ in the weak-star topology on the operator space $\operatorname{End}C^*(\Omega)$. The main results are formulated for ordinary (having metrizable semigroup $E$) semicascades and for tame dynamical systems determined by the condition $\operatorname{card}E\le\mathfrak c$. A classification of compact semicascades in terms of topological properties of the semigroups specified above is given.
Keywords: semicascade, ergodic properties, nonchaotic dynamics, tame dynamical system, enveloping semigroup
Mots-clés : Choquet simplex. 
@article{FAA_2013_47_2_a10,
     author = {A. V. Romanov},
     title = {Ordinary {Semicascades} and {Their} {Ergodic} {Properties}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {92--96},
     publisher = {mathdoc},
     volume = {47},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2013_47_2_a10/}
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A. V. Romanov. Ordinary Semicascades and Their Ergodic Properties. Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 2, pp. 92-96. http://geodesic.mathdoc.fr/item/FAA_2013_47_2_a10/