Let (Σ,ϱ) be the one-sided symbolic space (with two symbols), and let σ be the shift on Σ. We use A(·), R(·) 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-Smítal) and there is a strongly chaotic set 𝒥 satisfying 𝒥 ⊂ R(σ)-A(σ).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap78-2-3,
author = {Lidong Wang and Gongfu Liao and Yu Yang},
title = {Recurrent point set of the shift on $\Sigma$ and strong chaos},
journal = {Annales Polonici Mathematici},
volume = {79},
year = {2002},
pages = {123-130},
zbl = {1067.37011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap78-2-3}
}
Lidong Wang; Gongfu Liao; Yu Yang. Recurrent point set of the shift on Σ and strong chaos. Annales Polonici Mathematici, Tome 79 (2002) pp. 123-130. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap78-2-3/