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Regular version of the site

Article

Ordinary Semicascades and Their Ergodic Properties

Functional Analysis and Its Applications. 2013. Vol. 47. No. 2. P. 160-163.

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 Kohler 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  End C*(Ω). The main results are formulated for ordinary (having metrizable semigroup E) semicascades and for tame dynamical systems determined by the condition card E ≤ c. A classification of compact semicascades in terms of topological properties of the semigroups specified above is given.