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Chaoticity of interval self-maps with positive entropy.

机译:具有正熵的区间自映射的混沌性。

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Li and Yorke originally introduced the notion of chaos for continuous self-map of the interval I = (0,1). In the present paper we show that an interval self-map with positive topological entropy has a chaoticity more complicated than the chaoticity in the sense of Li and Yorke. The main result is that if f:I -> I is continuous and has a periodic point with odd period > 1 then there exists a closed subset K of I invariant with respect to f such that the periodic points are dense in K, the periods of periodic points in K form an infinite set and f K is topologically mixing. (author). 9 refs. (Atomindex citation 20:049818)

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