In this talk I will introduce the relations of rigidity, equicontinuity and pointwise recurrence between an invertible topological dynamical system (X; T) and the dynamical system (K(X); T_K) induced on the hyperspace K(X) of all compact subsets of X, and show some
characterizations.
Based on joint work with Piotr Oprocha, Xiangdong Ye and Ruifeng Zhang.