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

摘要

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)(infinity) in a metric space (X, d). It is shown that three versions named DC1, DC2, and DC21/2 are invariants under iterations when {f(n)}(n=0)(infinity) is equi-continuous in X, which weakens the condition in the literature that {f(n)}(n=0)(infinity) uniformly converges in a compact space X. It is also proved that DC1, DC2, and DC21/2 are invariants of topological equi-conjugacy. One example is provided with computer simulations for illustration. (C) 2018 Elsevier B.V. All rights reserved.