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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
Abstract
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.
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- Copyright © Australian Mathematical Society 1989
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