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.
Keywords : hyperspace, expansiveness, $N$-expansiveness, countable expansiveness, continuum-wise expansiveness, stable set
MSC numbers : 37B05, 37C45, 37D20, 54H20, 54B20
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