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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 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 PDF
Proc. Amer. Math. Soc. 113 (1991), 551-555 Request permission

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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Additional 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