On distributional chaos in non-autonomous discrete systems

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-Yorkeδ-chaotic if and only if it is distributionallyδ'-chaotic in a sequence; and three criteria of distributional δ-chaos are established, which are caused by topologically weak mixing, asymptotic average shadowing property, and some expanding condition, respectively, where δ and δ' are positive constants. In a general case, a criterion of distributional chaos in a sequence induced by a Xiong chaotic set is established.