Weakly almost periodicity and distributional chaos in a sequence. (English) Zbl 1186.37017

Summary: Let \((\Sigma, \rho)\) be a one-sided symbolic space (with two symbols) and \(\rho\) be the shift on \(\Sigma\). Denote the set of almost periodic points by \(A(\cdot)\) and the set of weakly almost periodic points by \(W(\cdot)\). In this paper, we prove that there exists an uncountable set \(J\) such that \(\sigma|J\) is distributively chaotic in a sequence, and \(J\subset W(\sigma)-A(\sigma)\).


37B10 Symbolic dynamics
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[1] Zhou Z. L., Sci. China (A) 22 pp 572–
[2] Schweizer B., Trans. Amer. Math. Soc. 334 pp 737–
[3] Devaney R. L., An Introduction to Chaotic Dynamical Systems (1989) · Zbl 0695.58002
[4] Wang L., Annls. Polonici Mathematici LXX VIII 2 pp 123–
[5] Yang R., Acta Mathematica Sinic 45 pp 753–
[6] Jiang H. J., J. Math. (PRC) 19 pp 56–
[7] DOI: 10.2307/2318254 · Zbl 0351.92021
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