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DC3 and Li-Yorke chaos. (English) Zbl 1311.37027

Summary: There are three versions of distributional chaos, namely DC1, DC2 and DC3. By using an example of constant-length substitution system, we show that DC3 need not imply Li-Yorke chaos. (In this paper, chaos means the existence of an uncountable scrambled set of the corresponding type, while the existing example only deals with a single pair of points.)

MSC:

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