Preservation of expansivity in hyperspace dynamical systems
J. Korean Math. Soc. Published online August 20, 2021
Namjip Koo and Hyunhee Lee
Chungnam National University; Chungnam National University
Abstract : In this paper we study the preservation of various notions of expansivity in discrete dynamical systems and the induced map for $n$-fold symmetric products and hyperspaces. Also we prove that there are no hyper $N$-expansive homeomorphisms on a compact manifold. Thus we give a characterization of a compact metric space admitting hyper $N$-expansive homeomorphisms via the topological dimension. Furthermore we give some examples to illustrate our results.