The equivalence relationship between Li-Yorke $δ$-chaos and distributional $δ$-chaos in a sequence

Details The equivalence relationship between Li-Yorke $δ$-chaos and distributional $δ$-chaos in a sequence The equivalence relationship between Li-Yorke $δ$-chaos and distributional $δ$-chaos in a sequence

2010-12-26

arxiv.org/abs/1012.5510v1

J. South China Normal Univ. Natur. Sci. Ed., 2010, no. 3, 34-38

Mathematics

Dynamical Systems

6 pages

Scientific paper

In this paper, we discuss the relationship between Li-Yorke chaos and distributional chaos in a sequence. We point out the set of all distributional $\delta$-scramble pairs in the sequence $Q$ is a $G_\delta$ set, and prove that Li-Yorke $\delta$-chaos is equivalent to distributional $\delta$-chaos in a sequence, a uniformly chaotic set is a distributional scramble set in some sequence and a class of transitive system implies distributional chaos in a sequence.

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