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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 \(J\subset W(\sigma)-A(\sigma)\).

MSC:

37B10 Symbolic dynamics
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References:

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[7] DOI: 10.2307/2318254 · Zbl 0351.92021
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