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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On noncontinuous chaotic functions
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by Jack Ceder
Proc. Amer. Math. Soc. 113 (1991), 551-555
DOI: https://doi.org/10.1090/S0002-9939-1991-1062384-8

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 $[0,1]$.
References
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Bibliographic Information
  • © Copyright 1991 American Mathematical Society
  • 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