On mixing property in set-valued discrete systems

Let (X, d) be a compact metric space and f : X → X be a continuous map. Let ( be the space of all non-empty compact subsets of X endowed with the Hausdorff metric induced by d and be the map defined by . In this paper we investigate the relationships between the mixing property of and the mixing property of (X, f). In addition, we discuss specification for the set-valued discrete dynamical system .