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

Jian Li; Feng Tan

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

Dynamical Systems 2011-05-20 v1

Authors: Jian Li , Feng Tan

Abstract

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.

Keywords

li-yorke chaos distributional chaos sequence g-delta set transitive system

Cite

@article{arxiv.1012.5510,
  title  = {The equivalence relationship between Li-Yorke $\delta$-chaos and distributional $\delta$-chaos in a sequence},
  author = {Jian Li and Feng Tan},
  journal= {arXiv preprint arXiv:1012.5510},
  year   = {2011}
}

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6 pages

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

Abstract

Keywords

Cite

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