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...
Saved in:
Published in | Acta mathematica Sinica. English series Vol. 31; no. 4; pp. 637 - 646 |
---|---|
Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Heidelberg
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
01.04.2015
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
Cover
Loading…
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 ObjectType-Feature-2 content type line 23 |
ISSN: | 1439-8516 1439-7617 |
DOI: | 10.1007/s10114-015-4202-z |