Li-Yorke chaos in a class of nonautonomous discrete systems

Let f(1,infinity) = (f(n)) be a sequence of continuous interval maps which converges uniformly to a continuous map f. We study the limit behaviour of sequences with the form (fn circle ... circle f(1))(x), x is an element of [0, 1], and whether the simplicity (respectively chaoticity) of f implies the simplicity (respectively chaoticity) of f(1,infinity).