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Zbl 1106.37008
Shi, Yuming; Yu, Pei
Study on chaos induced by turbulent maps in noncompact sets. (English)
[J] Chaos Solitons Fractals 28, No. 5, 1165-1180 (2006). ISSN 0960-0779

Summary: This paper is concerned with chaos induced by strictly turbulent maps in noncompact sets of complete metric spaces. Two criteria of chaos for such types of maps are established, and then a criterion of chaos, characterized by snap-back repellers in complete metric spaces, is obtained. All the maps presented in this paper are proved to be chaotic either in the sense of both Li-Yorke and Wiggins or in the sense of both Li-Yorke and Devaney. The results weaken the assumptions in some existing criteria of chaos. Several illustrative examples are provided with computer simulation.

MSC 2000:: *37B05 Transformations and group actions with special properties
37D45 Strange attractors, chaotic dynamics

Keywords: complete metric spaces; chaos; snap-back repellers

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