Some Dynamical Properties of Syndetic Subsemigroups Actions

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• 作者：Huoyun Wang (1) (2)
  Guifang Zhu (1)
  Yao Tang (1)
  Ling Huang (1)
  
  1. Department of Mathematics ; Guangzhou University ; Guangzhou ; 510006 ; People鈥檚 Republic of China
  2. Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes ; Guangzhou University ; Guangzhou ; 510006 ; People鈥檚 Republic of China
  
• 关键词：Semigroup actions ; Syndetic set ; Almost periodic points ; Totally transitive ; 37B05 ; 37B99 ; 54H20
• 刊名：Journal of Dynamical and Control Systems
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：21
• 期：1
• 页码：147-154
• 全文大小：170 KB
• 参考文献：1. Aking E, Glasner E. Residual properties and almost equicontinuity. J Anal Math 2001;84:243鈥?86. CrossRef
  2. Banks J. Regular periodic decompositions for topologically transitive maps. Ergodic Theorey Dynam System 1997;17:505鈥?29. CrossRef
  3. Ellis DB, Ellis R, Nerurkar M. The topological dynamics of semigroup actions. Trans Amer Math Soc 2000;353:1279鈥?320. CrossRef
  4. Ceccherini-Silbertstein T, Coornaert M. Sensitivity and Devaney鈥檚 definition of chaos in uniform spaces. J Dyn Control Syst 2013;19:349鈥?57. CrossRef
  5. Furstenberg H. Recurrence in ergodic theory and combinational number theory. Princeton: Princeton University Press; 1981.
  6. Kontorovich E, Megrelishvili M. A note on sensitivity of semigroup actions. Semigroup Forum 2008;76:133鈥?41. CrossRef
  7. Miller A. Envelopes of syndetic subsemigroups of the acting topological semigroup in a semiflow. Topology and its Applications 2011;158:291鈥?97. CrossRef
  8. Schneider FM, Kerkhoff S, Behrisch M, Siegmund S. Chaotic actions of topological semigroups. Semigroup Forum 2013;87:590鈥?98. CrossRef
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Calculus of Variations and Optimal Control
  Analysis
  Applications of Mathematics
  Systems Theory and Control
  
• 出版者：Springer Netherlands
• ISSN：1573-8698

文摘

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.