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Continuous chaotic functions of an interval have generically small scrambled sets

Published online by Cambridge University Press:  17 April 2009

Ivan Mizera
Ivan Mizera
Affiliation:
Department of Mathematics, Komensk University842 15 Bratislava, Czechoslovakia
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Abstract

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It is shown that continuous self-mappings of a compact interval, chaotic in the sense of Li and Yorke, have generically, in the uniform topology, only scrambled sets which are nowhere dense and of zero Lebesgue measure.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 1 , February 1988 , pp. 89 - 92
Copyright
Copyright Australian Mathematical Society 1988

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