Some Dynamical Properties of Syndetic Subsemigroups Actions
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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.
KeywordsSemigroup actions Syndetic set Almost periodic points Totally transitive
Mathematics Subject Classification (2010)37B05 37B99 54H20
We are grateful to the reviewers for the useful comments. The research of H. Wang was supported by National Nature Science Funds of China (11326135) and Guangzhou Education Bureau (2012A075).
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