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Every chaotic interval map has a scrambled set in the recurrent set

Published online by Cambridge University Press:  17 April 2009

Bau-Sen Du
Bau-Sen Du
Affiliation:
Institute of Mathematics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
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Abstract

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Let I denote a compact real interval and let f ∈ C0(I, I). In this note we show that if f chaotic in the sense of Li and Yorke, then there is an uncountable perfect δ-scrambled set S for f in the recurrent set of f. Furthermore, the ω-limit set of every x ∈ S under f contains S and contains infinitely many periodic points of f with arbitrarily large periods.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 39 , Issue 2 , April 1989 , pp. 259 - 264
Copyright
Copyright © Australian Mathematical Society 1989

References

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