Some weak versions of distributional chaos in non-autonomous discrete systems.

Highlights • DC 1, 2, and 5/2 are invariants under iterations in non-autonomous discrete systems. • DC 1, 2, and 5/2 are invariants of topological equi-conjugacy in non-autonomous discrete systems. • Instead of uniformly convergent sequence of maps, a sequence of equi-continuous maps are considered. • Those related existing results are generalized to non-autonomous systems. Abstract This paper is concerned with some weak versions of distributional chaos in a non-autonomous discrete system generated by a given sequence of maps { f n } n = 0 ∞ in a metric space (X, d). It is shown that three versions named DC1, DC2, and DC 2 1 2 are invariants under iterations when { f n } n = 0 ∞ is equi-continuous in X , which weakens the condition in the literature that { f n } n = 0 ∞ uniformly converges in a compact space X. It is also proved that DC1, DC2, and DC 2 1 2 are invariants of topological equi-conjugacy. One example is provided with computer simulations for illustration. [ABSTRACT FROM AUTHOR]

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