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Study on chaos induced by turbulent maps in noncompact sets. (English) Zbl 1106.37008
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:
 37B05 Transformations and group actions with special properties 37D45 Strange attractors, chaotic dynamics
##### Keywords:
complete metric spaces; chaos; snap-back repellers