Minimal periodic orbits of continuous mappings of the circle

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 {p1, pn} is minimal if its period is n. 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 φ(n) types of minimal periodic orbits of period n, where <p is the Euler phi-function. © 1981 American Mathematical Society.