3-PERIODIC ORBIT IMPLYING 6831726876986508 85-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 greater-than-or-equal-to 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 continuous function on I, and N(m, f) greater-than-or-equal-to 1}. The famous Sarkovskii's theorem can be stated as follows: If n is part of m, then N(n,m) greater-than-or-equal-to 1. In this paper, we further obtain analytic expressions of the precise value of N(n, m) for all positive integers m and n, which are convenient for computing.