Sensitivity for set-valued maps induced by M-systems

Bingzhe Hou, Gongfu Liao and Heng Liu

Chaos, Solitons & Fractals, 2008, vol. 38, issue 4, 1075-1080

Abstract: Consider a continuous map f:X→X and the continuous map f¯ of K(X) into itself induced by f, where X is a compact metric space without isolated points and K(X) is the space of all non-empty compact subsets of X endowed with a Hausdorff metric. In this paper, we discuss the sensitivity of the set valued maps induced by M-systems. In fact, we prove that if (X,f) is a non-minimal M-system, then f¯ is sensitive; and give an example to show the possibility that f¯ is sensitive when (X,f) is a, minimal but not weakly mixing, M-system.

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:38:y:2008:i:4:p:1075-1080

DOI: 10.1016/j.chaos.2007.02.015

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