论文信息 - On Three Definitions of Chaos

On Three Definitions of Chaos

We discuss in this paper three notions of chaos which are com- monly used in the mathematical literature, namely those being introduced by Li & Yorke, Block & Coppel and Devaney, respectively. We in particular show that for continuous mappings of a compact interval into itself the no- tions of chaos due to Block & Coppel and Devaney are equivalent while each of these is sufficient but not necessary for chaos in the sense of Li & Yorke. We also give an example indicating that in the general context of continuous mappings between compact metric spaces the relation between these three notions of chaos is more involved.

B. Aulbach | Bernd Aulbach | Bernd Kieninger | Bernd Kieninger

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