Sensitivity of set-valued discrete systems

Abstract

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