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Proceedings of the American Mathematical Society

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

 

 

Periods of periodic points of maps of the circle which have a fixed point


Author: Louis Block
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0612745-7
Article copyright: © Copyright 1981 American Mathematical Society