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Erschienen in:
01.01.2015
Some Dynamical Properties of Syndetic Subsemigroups Actions
Erschienen in: Journal of Dynamical and Control Systems | Ausgabe 1/2015
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Abstract
In this paper, some dynamical properties of syndetic subsemigroups actions are studied. We prove that for any s-syndetic subsemigroup T of the acting abelian semigroup S equipped with the discrete topology, the set of all almost periodic points of T is equal to the set of all almost periodic points of S. We deduce some statements on decomposition for point transitive semigroup actions by envelopes of g-syndedic subsemigroup. A transitive dynamical system (S,X) is called totally transitive if (T,X) is transitive for every syndetic subsemigroup T of S. We point out that a dynamical system (S,X) is totally transitive if and only if it is weakly disjoint from every s-periodic system, where S contains an identity and every s of S is a surjective map from X onto itself.