Recurrent point set of the shift on \({\varSigma}\) and strong chaos. (English) Zbl 1067.37011

Wang, Lidong; Liao, Gongfu; Yang, Yu

Ann. Pol. Math. 78, No. 2, 123-130 (2002).

Summary: Let \(({\varSigma},\varrho)\) be the one-sided symbolic space (with two symbols), and let \(\sigma\) be the shift on \({\varSigma}\). We use \(A(\cdot)\), \(R(\cdot)\) to denote the set of almost periodic points and the set of recurrent points, respectively. Here, we prove that the one-sided shift is strongly chaotic (in the sense of Schweizer-Smítal) and there is a strongly chaotic set \({\mathcal J}\) satisfying \({\mathcal J}\subset R(\sigma)-A(\sigma)\).

MSC:

37B10	Symbolic dynamics
37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior

Keywords:

recurrent point; shift; strong chaos