Abstract
We give a class C of continuous functions from [0, 1] onto itself which are chaotic in the sense of Li and Yorke, but with the property that almost all (in the sense of Lebesgue) points of [0, 1] are eventually fixed. For some continuous functions from [0, 1] onto itself which are not in C, We also show that their non-wandering sets are all equal to the interval [0, 1].
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