Devaney Chaos for the Functional Envelope of a Nonautonomous Discrete Dynamical System

Abstract

This paper investigates Devaney chaos in the L1-functional envelope system associated with a nonautonomous discrete dynamical system. We prove that if (I,f∞) is weakly mixing of order 3, then its L1-functional envelope system is weakly mixing of all orders. Moreover, if, in addition, the periodic points of (I,f∞) are dense in I, then the functional envelope system (L1(I,I),H∞) is Devaney chaotic.