Abstract
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.
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Supported by National Natural Science Foundation of China (Grant No. 11261039), National Natural Science Foundation of Jiangxi Province (Grant No. 20132BAB201009) and the Innovation Fund Designated for Graduate Students of Jiangxi Province
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Yan, Q., Yin, J.D. & Wang, T. A note on quasi-weakly almost periodic point. Acta. Math. Sin.-English Ser. 31, 637–646 (2015). https://doi.org/10.1007/s10114-015-4202-z
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DOI: https://doi.org/10.1007/s10114-015-4202-z