Sensitivity for set-valued maps induced by M-systems

Consider a continuous map f:X→X and the continuous map f-bar of K(X) into itself induced by f, where X is a compact metric space without isolated points and K(X) is the space of all non-empty compact subsets of X endowed with a Hausdorff metric. In this paper, we discuss the sensitivity of the set valued maps induced by M-systems. In fact, we prove that if (X,f) is a non-minimal M-system, then f-bar is sensitive; and give an example to show the possibility that f-bar is sensitive when (X,f) is a, minimal but not weakly mixing, M-system