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 be a continuous map of the circle into itself and suppose that is the least integer which occurs as a period of a periodic orbit of . Then we say that a periodic orbit is minimal if its period is . We classify the minimal periodic orbits, that is, we describe how the map must act on the minimal periodic orbits. We show that there are types of minimal periodic orbits of period , where 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