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Recurrent point set of the shift on ${\mit \Sigma }$ and strong chaos

Tom 78 / 2002

Lidong Wang, Gongfu Liao, Yu Yang Annales Polonici Mathematici 78 (2002), 123-130 MSC: 58F13, 58F20. DOI: 10.4064/ap78-2-3

Streszczenie

Let $({\mit \Sigma },\varrho )$ be the one-sided symbolic space (with two symbols), and let $\sigma $ be the shift on ${\mit \Sigma }$. We use $A(\cdot )$, $R(\cdot )$ to denote the set of almost periodic points and the set of recurrent points respectively. In this paper, we prove that the one-sided shift is strongly chaotic (in the sense of Schweizer–Sm{í}tal) and there is a strongly chaotic set ${\cal J}$ satisfying ${\cal J}\subset R(\sigma )-A(\sigma )$.

Autorzy

  • Lidong WangDepartment of Mathematics
    Dalian University for National Minorities
    Dalian 116600, P.R. China
  • Gongfu LiaoDepartment of Mathematics
    Jilin University
    Changchun 130023, P.R. China
    e-mail
  • Yu YangDepartment of Computer Science
    Siping Teacher's College
    Siping 136000, P.R. China

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