Periods of Periodic Points of Maps of the Circle which Have a Fixed Point
- 1 July 1981
- journal article
- Published by JSTOR in Proceedings of the American Mathematical Society
- Vol. 82 (3) , 481-486
- https://doi.org/10.2307/2043966
Abstract
For a continuous map of the circle to itself, let denote the set of positive integers such that has a periodic point of (least) period . Results are obtained which specify those sets, which occur as , for some continuous map 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.Keywords
This publication has 3 references indexed in Scilit:
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- Periodic points and topological entropy of one dimensional mapsPublished by Springer Nature ,1980
- A theorem of Šarkovskii on the existence of periodic orbits of continuous endomorphisms of the real lineCommunications in Mathematical Physics, 1977