Chaos in hyperspace system

Xianfeng Ma, Bingzhe Hou and Gongfu Liao

Chaos, Solitons & Fractals, 2009, vol. 40, issue 2, 653-660

Abstract: Let (X,d) be a compact metric space and f:X→X be continuous. Let f¯ be the natural extension of f to the space of all non-empty compact subsets of X endowed with the Hausdorff metric induced by d. In this paper, some dynamical properties of f and f¯ are considered. It is shown that positive topological entropy, Li–Yorke chaos and distributional chaos of f imply those of f¯, respectively, but not conversely. The results give an answer to the question proposed by Román-Flores.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:40:y:2009:i:2:p:653-660

DOI: 10.1016/j.chaos.2007.08.009

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