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Published in: Journal of Dynamical and Control Systems 1/2015

01-01-2015

Some Dynamical Properties of Syndetic Subsemigroups Actions

Authors: Huoyun Wang, Guifang Zhu, Yao Tang, Ling Huang

Published in: Journal of Dynamical and Control Systems | Issue 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.

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Literature
2.
go back to reference Banks J. Regular periodic decompositions for topologically transitive maps. Ergodic Theorey Dynam System 1997;17:505–529.CrossRefMATH Banks J. Regular periodic decompositions for topologically transitive maps. Ergodic Theorey Dynam System 1997;17:505–529.CrossRefMATH
3.
go back to reference Ellis DB, Ellis R, Nerurkar M. The topological dynamics of semigroup actions. Trans Amer Math Soc 2000;353:1279–1320.CrossRefMathSciNet Ellis DB, Ellis R, Nerurkar M. The topological dynamics of semigroup actions. Trans Amer Math Soc 2000;353:1279–1320.CrossRefMathSciNet
4.
go back to reference Ceccherini-Silbertstein T, Coornaert M. Sensitivity and Devaney’s definition of chaos in uniform spaces. J Dyn Control Syst 2013;19:349–357.CrossRefMathSciNet Ceccherini-Silbertstein T, Coornaert M. Sensitivity and Devaney’s definition of chaos in uniform spaces. J Dyn Control Syst 2013;19:349–357.CrossRefMathSciNet
5.
go back to reference Furstenberg H. Recurrence in ergodic theory and combinational number theory. Princeton: Princeton University Press; 1981. Furstenberg H. Recurrence in ergodic theory and combinational number theory. Princeton: Princeton University Press; 1981.
7.
go back to reference Miller A. Envelopes of syndetic subsemigroups of the acting topological semigroup in a semiflow. Topology and its Applications 2011;158:291–297.CrossRefMATHMathSciNet Miller A. Envelopes of syndetic subsemigroups of the acting topological semigroup in a semiflow. Topology and its Applications 2011;158:291–297.CrossRefMATHMathSciNet
8.
Metadata
Title
Some Dynamical Properties of Syndetic Subsemigroups Actions
Authors
Huoyun Wang
Guifang Zhu
Yao Tang
Ling Huang
Publication date
01-01-2015
Publisher
Springer US
Published in
Journal of Dynamical and Control Systems / Issue 1/2015
Print ISSN: 1079-2724
Electronic ISSN: 1573-8698
DOI
https://doi.org/10.1007/s10883-014-9246-3

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