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There are no chaotic mappings with residual scrambled sets

Published online by Cambridge University Press:  17 April 2009

T. Gedeon
T. Gedeon
Affiliation:
Katedra algebry, Faculty of Mathematics and Physics, Komensky University, 842 15 Bratislava, Czecholovakia.
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A continuous mapping f of a compact real interval I to itself which is chaotic in the sense of Li and Yorke, cannot have a scrambled set residual in an subinterval of I. This shows that chaos in this case cannot be large from a topological point of view.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 3 , December 1987 , pp. 411 - 416
Copyright
Copyright © Australian Mathematical Society 1987

References

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