The set-valued mapping induced by a non-minimal transitive system is Li–Yorke chaotic

Heng Liu, Gongfu Liao and Bingzhe Hou

Chaos, Solitons & Fractals, 2009, vol. 40, issue 2, 826-830

Abstract: Let X be a metric space, (X,f) a discrete dynamical system, where f: X→X is a continuous function. Let f¯ denote the natural extension of f to the space of all non-empty compact subsets of X endowed with a Hausdorff metric. In this paper, we prove that if f is transitive and non-minimal, then f¯ is Li–Yorke’s chaos. Furthermore, if f is non-minimal M-system, then f¯ has a s-scrambled set.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:40:y:2009:i:2:p:826-830

DOI: 10.1016/j.chaos.2007.08.030

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