Chaos in a class of non-autonomous discrete systems

Let f 1 , ∞ = ( f n ) n = 1 ∞ be a sequence of continuous maps defined on a compact metric space which converges uniformly to a map f . We prove that the chaotic behaviour of sequences with the form ( f n ∘ ⋯ ∘ f 1 ) ( x ) is inherited under iterations.