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

 

On noncontinuous chaotic functions


Author: Jack Ceder
Journal: Proc. Amer. Math. Soc. 113 (1991), 551-555
MSC: Primary 26A18
MathSciNet review: 1062384
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Abstract: A function $ f:[0,1] \to [0,1]$ is constructed such that for each two distinct points $ x$ and $ y$ in $ [0,1]$ the sequence $ \left\{ {\left\vert {{f^n}(x) - {f^n}(y)} \right\vert} \right\}_{n = 0}^\infty $ is dense in $ [0,1]$. Here $ {f^n}$ is the $ n$th iterate of $ f$. Moreover a Baire 2 function can be constructed so that the above condition is valid for all distinct $ x$ and $ y$ in a dense open subset of $ [0,1]$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1062384-8
PII: S 0002-9939(1991)1062384-8
Article copyright: © Copyright 1991 American Mathematical Society