A Note on Quasi-weakly Almost Periodic Point

Recently, He et al. [On quasi-weakly almost periodic points. Sci. China Math., 56, 597- 606 （2013）] constructed two binary sub-shifts to solve an open problem posed by Zhou and Feng in [Twelve open problems on the exact value of the Hausdorff measure and on topological entropy： A brief survey of rec...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 31; no. 4; pp. 637 - 646
Main Authors Yan, Qi, Yin, Jian Dong, Wang, Tao
Format Journal Article
LanguageEnglish
Published Heidelberg Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.04.2015
Springer Nature B.V
Subjects
China
Construction
Dynamical systems
Entropy
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Studies
Topological manifolds
Topology
中国数学
动力学性质
开放式
开放性问题
弱几乎周期点
拓扑熵
注记
豪斯多夫测度
37D45
weakly almost periodic point
37B40
quasi-weakly almost periodic point
Topological entropy
strongly mixing
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Summary:Recently, He et al. [On quasi-weakly almost periodic points. Sci. China Math., 56, 597- 606 （2013）] constructed two binary sub-shifts to solve an open problem posed by Zhou and Feng in [Twelve open problems on the exact value of the Hausdorff measure and on topological entropy： A brief survey of recent results. Nonlinearity, 17, 493-502 （2004）]. In this paper, we study more dynamical properties of those two binary sub-shifts. We show that the first one has zero topological entropy and is transitive but not weakly mixing, while the second one has positive topological entropy and is strongly mixing.
Bibliography:11-2039/O1
Recently, He et al. [On quasi-weakly almost periodic points. Sci. China Math., 56, 597- 606 （2013）] constructed two binary sub-shifts to solve an open problem posed by Zhou and Feng in [Twelve open problems on the exact value of the Hausdorff measure and on topological entropy： A brief survey of recent results. Nonlinearity, 17, 493-502 （2004）]. In this paper, we study more dynamical properties of those two binary sub-shifts. We show that the first one has zero topological entropy and is transitive but not weakly mixing, while the second one has positive topological entropy and is strongly mixing.
Topological entropy, weakly almost periodic point, quasi-weakly almost periodic point,strongly mixing
ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-015-4202-z