Recurrent point set of the shift on ${\mit \Sigma }$ and strong chaos
Tom 78 / 2002
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 ${\cal J}\subset R(\sigma )-A(\sigma )$.
