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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Periods of periodic points of maps of the circle which have a fixed point
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by Louis Block PDF
Proc. Amer. Math. Soc. 82 (1981), 481-486 Request permission

Abstract:

For a continuous map $f$ of the circle to itself, let $P(f)$ denote the set of positive integers $n$ such that $f$ has a periodic point of (least) period $n$. Results are obtained which specify those sets, which occur as $P(f)$, for some continuous map $f$ of the circle to itself having a fixed point. These results extend a theorem of Šarkovskii on maps of the interval to maps of the circle which have a fixed point.
References
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 82 (1981), 481-486
  • MSC: Primary 58F20; Secondary 54H20
  • DOI: https://doi.org/10.1090/S0002-9939-1981-0612745-7
  • MathSciNet review: 612745