Invariant scrambled sets and maximal distributional chaos

Volume 109 / 2013

Xinxing Wu, Peiyong Zhu Annales Polonici Mathematici 109 (2013), 271-278 MSC: Primary 37D45, 54H20, 37B40; Secondary 26A18, 28D20. DOI: 10.4064/ap109-3-3

Abstract

For the full shift $(\varSigma _{2}, \sigma )$ on two symbols, we construct an invariant distributionally $\epsilon $-scrambled set for all $0<\epsilon < \operatorname{diam} \varSigma _{2}$ in which each point is transitive, but not weakly almost periodic.

Authors

  • Xinxing WuSchool of Mathematics
    University of Electronic Science
    and Technology of China
    Chengdu, Sichuan, 611731
    People's Republic of China
    and
    Department of Electronic Engineering
    City University of Hong Kong
    Hong Kong SAR
    People's Republic of China
    e-mail
  • Peiyong ZhuSchool of Mathematics
    University of Electronic Science
    and Technology of China
    Chengdu, Sichuan, 611731
    People's Republic of China
    e-mail

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