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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
DOI: https://doi.org/10.1090/S0002-9939-1991-1062384-8
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 $\left \{ {\left | {{f^n}(x) - {f^n}(y)} \right |} \right \}_{n = 0}^\infty$ 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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Article copyright: © Copyright 1991 American Mathematical Society