AN EXTENSION OF SARKOVSKII THEOREM TO THE N-OD

The n-od is defined to be the set of all complex numbers z such that z(n) is a real number in the interval [0, 1], i.e., a central point with n copies of the unit interval attached at their endpoints. Given a space X and a function f:X --> X, Per (f) is defined to be the set {k:f has for a point of (least) period k, k a positive integer}. The main result of this paper is to give, for each n, a complete characterization of all possible sets Per (f), where f ranges over all continuous functions on the n-od.