3-PERIODIC ORBIT IMPLYING 683172687698650885-PERIODIC ORBITS——INFIMUMS OF NUMBERS OF PERIODIC ORBITS IN CONTINUOUS FUNCTIONS

For any continuous function f on the interval I=[0, 1] and any m, n≥1, let N(n, f)denote the number of n-periodic orbits in f. Put N(n, m)=min{N(n, f):f is a continuousfunction on I, and N(m, f)≥1}. The famous Sarkovskii’s theorem can be stated as follows:If n?m, then N(n,m)≥1. In this paper, we further obtain analytic expressions of the precisevalue of N(n, m) for all positive integers m and n, which are convenient for computing.