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Chaotic difference equations are dense

Published online by Cambridge University Press:  17 April 2009

Peter E. Kloeden
Peter E. Kloeden
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria.
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Abstract

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A continuous function mapping a compact interval of the real line into itself is called chaotic if the difference equation defined in terms of it behaves chaotically in the sense of Li and Yorke. The set of all such chaotic functions is shown to toe a dense subset of the space of continuous mappings of that interval into itself with the max norm. This result indicates the structural instability of nonchaotic difference equations with respect to chaotic behaviour.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 15 , Issue 3 , December 1976 , pp. 371 - 379
Copyright
Copyright © Australian Mathematical Society 1976

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