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Proceedings of the American Mathematical Society

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

 
 

 

Minimal periodic orbits of continuous mappings of the circle


Author: Jaume Llibre
Journal: Proc. Amer. Math. Soc. 83 (1981), 625-628
MSC: Primary 54H20; Secondary 58F20
DOI: https://doi.org/10.1090/S0002-9939-1981-0627708-5
MathSciNet review: 627708
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Abstract: Let $ f$ be a continuous map of the circle into itself and suppose that $ n > 1$ is the least integer which occurs as a period of a periodic orbit of $ f$. Then we say that a periodic orbit $ \{ {p_1}, \ldots ,{p_n}\} $ is minimal if its period is $ n$. We classify the minimal periodic orbits, that is, we describe how the map $ f$ must act on the minimal periodic orbits. We show that there are $ \varphi (n)$ types of minimal periodic orbits of period $ n$, where $ \varphi $ is the Euler phi-function.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0627708-5
Article copyright: © Copyright 1981 American Mathematical Society

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