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Shi, Yuming; Chen, Guanrong

Chaos of discrete dynamical systems in complete metric spaces. (English) Zbl 1067.37047

Chaos Solitons Fractals 22, No. 3, 555-571 (2004).
Summary: This paper is concerned with chaos of discrete dynamical systems in complete metric spaces. Discrete dynamical systems governed by continuous maps in general complete metric spaces are first discussed, and two criteria of chaos are then established. As a special case, two corresponding criteria of chaos for discrete dynamical systems in compact subsets of metric spaces are obtained. These results extend and improve the existing relevant results of chaos in finite-dimensional Euclidean spaces.

Cited in 77 Documents

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
54E40 Special maps on metric spaces

Keywords:

chaotic problems in infinite-dimensional spaces
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\textit{Y. Shi} and \textit{G. Chen}, Chaos Solitons Fractals 22, No. 3, 555--571 (2004; Zbl 1067.37047)
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References:

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