Minimal Periodic Orbits of Continuous Mappings of the Circle

Let be a continuous map of the circle into itself and suppose that 1$"> is the least integer which occurs as a period of a periodic orbit of . Then we say that a periodic orbit <!-- MATH $\{ {p_1}, \ldots ,{p_n}\}$ --> 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 <!-- MATH $\varphi (n)$ --> types of minimal periodic orbits of period , where is the Euler phi-function.