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

Abstract

For a continuous map f f of the circle to itself, let P ( f ) P(f) denote the set of positive integers n n such that f f has a periodic point of (least) period n n . Results are obtained which specify those sets, which occur as P ( f ) P(f) , for some continuous map f 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.