On the Devaney chaos of non-autonomous discrete dynamical systems

This paper investigates Devaney chaos in non-autonomous discrete systems (NADSs). On one hand, the independence of the three conditions in the definition of Devaney chaos is discussed in NADSs. In the study of autonomous discrete systems, a fundamental and celebrated result concerning Devaney chaos is Banks theorem, which establishes that topological transitivity combined with the density of periodic points implies sensitivity to initial conditions. In this paper, the classical Banks theorem is generalized to equicontinuous NADSs. On the other hand, the invariance of Devaney chaos is examined from the perspectives of topological conjugacy and product operations. It is shown that Devaney chaos is preserved under topological conjugacy but not necessarily preserved under product operations in NADSs. A necessary and sufficient condition for Devaney chaos to be preserved under product operations is provided.