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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.