No division and the set of periods for tree maps

We extend the notion of no division for star maps to tree maps and prove that the set of periods of a tree map is cofinite if there exists some periodic orbit of the given map with period larger than one having no division. Using this result we obtain somesimple proofs of known results about the set of periods of a tree map. Also we show that this set is a union of initial segments of a finite number of linear orderings which depend only on the given tree minus a finite subset of N. © 1995, Cambridge University Press. All rights reserved.