Sensitivity of set-valued discrete systems

Consider the surjective, continuous map f:X→Xf:X→X and the continuous map f¯ of K(X)K(X) into itself induced by ff, where XX is a compact metric space and K(X)K(X) is the space of all non-empty compact subsets of XX endowed with a Hausdorff metric. In this paper we give examples showing that sensitivity of ff does not imply sensitivity of f¯. Furthermore, we prove that if ff is a surjective, continuous interval map, then f¯ is sensitive if and only if ff is sensitive.