Journal of University of Science and Technology of China ›› 2014, Vol. 44 ›› Issue (2): 93-95.DOI: 10.3969/j.issn.0253-2778.2014.02.002
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LI Jian
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Abstract: Let T be a continuous self-map of a compact metric space X. The transformation T induces naturally a continuous self-map TK on the hyperspace K(X) of all non-empty closed subsets of X. It is shown that the system (K(X),TK) is Devaney chaotic if and only if (K(X),TK) is an HY-system if and only if (X,T) is an HY-system, where a system is called an HY-system if it is totally transitive and has dense small periodic sets.
Key words: hyperspace, Devaney chaos, HY-system
LI Jian. Equivalent conditions of Devaney chaos on the hyperspace[J]. Journal of University of Science and Technology of China, 2014, 44(2): 93-95.
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URL: http://just-cn.ustc.edu.cn/EN/10.3969/j.issn.0253-2778.2014.02.002
http://just-cn.ustc.edu.cn/EN/Y2014/V44/I2/93