Dinámica colectiva

abstract. for a metric compact set x and a continuous map f : x → x we consider the hyperspace 2x of all closed and nonempty subsets of x with the hausdorff metric, and the induced map : 2x → 2x. in the past few years the study of the connection between the dynamical properties of ？ and those of has became an important and fruitful topic. in this paper we survey some significant results in this area. also we collect some open questions and conjectures.