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Ordinary semicascades and their ergodic properties

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Abstract

A relationship is considered between ergodic properties of a discrete dynamical system on a compact metric space Ω and characteristics of companion algebro-topological objects, namely, the Ellis enveloping semigroup E, the Köhler enveloping operator semigroup Γ, and the semigroup G being the closure of the convex hull of Γ in the weak-star topology on the operator space EndC*(Ω). The main results are formulated for ordinary (having metrizable semigroup E) semicascades and for tame dynamical systems determined by the condition cardE ⩽ c. A classification of compact semicascades in terms of topological properties of the semigroups specified above is given.

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Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    A. V. Romanov

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  1. A. V. Romanov
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Correspondence to A. V. Romanov.

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__________

Translated from Funktsional’ nyi Analiz i Ego Prilozheniya, Vol. 47, No. 2, pp. 92–96, 2013

Original Russian Text Copyright © by A. V. Romanov

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Romanov, A.V. Ordinary semicascades and their ergodic properties. Funct Anal Its Appl 47, 160–163 (2013). https://doi.org/10.1007/s10688-013-0022-z

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  • DOI: https://doi.org/10.1007/s10688-013-0022-z

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