Sensitive dependence for nonautonomous dynamical systems

Abstract

Given a nonautonomous discrete dynamical system (NDS) $(X,f_{1,\infty})$ we show that transitivity and density of periodic points do not imply sensitivity in general, i.e., in the definition of Devaney chaos there are no redundant conditions for NDS. In addition, we show that if we also assume uniform convergence of the sequence $(f_n)$ that induces the NDS, then sensitivity follows. Furthermore, in contrast to the autonomous case, we show that there exist minimal NDS which are neither equicontinuous nor sensitive.