Sensitivity for set-valued maps induced by M-systems

Consider a continuous map f:X→Xf:X→X and the continuous map f¯ of K(X)K(X) into itself induced by f, where X   is a compact metric space without isolated points and K(X)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)(X,f) is a non-minimal M  -system, then f¯ is sensitive; and give an example to show the possibility that f¯ is sensitive when (X,f)(X,f) is a, minimal but not weakly mixing, M-system.