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Chaos of discrete dynamical systems in complete metric spaces. (English) Zbl 1067.37047
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.
MSC:
37D45Strange attractors, chaotic dynamics
54E40Special maps on metric spaces