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Are chaotic functions really chaotic

Published online by Cambridge University Press:  17 April 2009

Bau-Sen Du
Bau-Sen Du
Affiliation:
School of Mathematics, University of Minnesota, 206 Church Street SE, Minneapolis, Minnesota 55455, USA.
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Abstract

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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].

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 28 , Issue 1 , August 1983 , pp. 53 - 66
Copyright
Copyright © Australian Mathematical Society 1983

References

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