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arXiv · 1801.04445

On distributional chaos in non-autonomous discrete systems

Hua Shao·Yuming Shi·Hao Zhu
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Abstract

This paper studies distributional chaos in non-autonomous discrete systems generated by given sequences of maps in metric spaces. In the case that the metric space is compact, it is shown that a system is Li-Yorke{\delta}-chaotic if and only if it is distributionally{\delta}'-chaotic in a sequence; and three criteria of distributional {\delta}-chaos are established, which are caused by topologically weak mixing, asymptotic average shadowing property, and some expanding condition, respectively, where {\delta} and {\delta}' are positive constants. In a general case, a criterion of distributional chaos in a sequence induced by a Xiong chaotic set is established.

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Hua Shao, Yuming Shi, Hao Zhu. 2018-01-13. On distributional chaos in non-autonomous discrete systems. https://doi.org/10.1016/j.chaos.2018.01.005

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