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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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A chaotic function whose nonwandering set is the Cantor ternary set
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Proc. Amer. Math. Soc. 92 (1984), 277-278 Request permission

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
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 92 (1984), 277-278
  • MSC: Primary 58F13; Secondary 26A30, 54H20
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0754720-0
  • MathSciNet review: 754720