The set of recurrent points of a continuous self-map on compact metric spaces and strong chaos

Tom 82 / 2003

Lidong Wang, Gongfu Liao, Zhizhi Chen, Xiaodong Duan Annales Polonici Mathematici 82 (2003), 265-272 MSC: 37B10, 37B40, 74H65, 34C28, 54H20. DOI: 10.4064/ap82-3-7

Streszczenie

We discuss the existence of an uncountable strongly chaotic set of a continuous self-map on a compact metric space. It is proved that if a continuous self-map on a compact metric space has a regular shift invariant set then it has an uncountable strongly chaotic set in which each point is recurrent, but is not almost periodic.

Autorzy

  • Lidong WangLidong Wang and Xiaodong Duan
    Research Institute of Nonlinear Information Technology
    Dalian Nationalities University
    Dalian 116600, P.R. China
    e-mail
  • Gongfu LiaoGongfu Liao
    Institute of Mathematics
    Jilin University
    Changchun 130023, P.R. China
    e-mail
  • Zhizhi ChenZhizhi Chen
    Graduate Department of Jilin Normal University
    Siping 136000, P.R. China
    e-mail
  • Xiaodong DuanLidong Wang and Xiaodong Duan
    Research Institute of Nonlinear Information Technology
    Dalian Nationalities University
    Dalian 116600, P.R. China
    e-mail

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