Ergodic Theory and Dynamical Systems

Research Article

An extension of Šarkovskiư's Theorem to the n-od

Stewart Baldwina1

a1 Division of Mathematics, Auburn University, Auburn, AL 36849–5310, USA

Abstract

The n-od is defined to be the set of all complex numbers z such that zn 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:XX, 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.

(Received September 02 1988)

(Revised September 18 1989)