Devaney Chaos for the Function Envelope of a Non-Autonomous Discrete Dynamical System

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This paper investigates Devaney chaos in the \(L^{1}\)-function envelope system associated with a nonautonomous discrete dynamical system. We prove that if (I, f∞) is weakly mixing of order 3, then its $L^1$-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 \((L^1(I,I),H_{\infty})\) is Devaney chaotic.

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