:In this paper, by supposing E to be the attractor of an iterated function system （X,f1,…,fN） which satisfies the strong separation condition, defining a continuous mapping f： E→Ef（x） =f -1j （x）, x x∈fj（E）, j = 1,..., N, and setting （p1 ,P2,…,PN） as a probability vector andμ the corresponding invariant measure, some complex dynamical behaviors of the continuous mapping are investigated. The results indicate that, for the mappingf, there exists a finitely chaotic set C CE satisfyingμ（C） =μ（E） = 1, and that the mapping f has some chaotic minimal subsystem with zero topological entropy in the sense of Li-Yorke. Some existing results are tinally generalized in the paper.