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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A chaotic function whose nonwandering set is the Cantor ternary set


Author: Bau Sen Du
Journal: Proc. Amer. Math. Soc. 92 (1984), 277-278
MSC: Primary 58F13; Secondary 26A30, 54H20
MathSciNet review: 754720
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Abstract: We introduce a continuous function from [0, 1] onto itself whose nonwandering set is the Cantor ternary set $ C$. This function is also chaotic in the sense of Li and Yorke, but with the property that almost all points of [0, 1] are eventually fixed. Those points of $ C$ which are periodic, eventually periodic, asymptotically periodic or recurrent are also explicitly identified.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0754720-0
PII: S 0002-9939(1984)0754720-0
Article copyright: © Copyright 1984 American Mathematical Society