Small periods of endomorphisms of trees

AbstractWe investigate some problems concerning a generalization of the theorem of S̆arkovskii for arbitrary trees. Among others, we show that, for a noncompact tree with at least three edges, the existence of periodic orbits does not imply the existence of fixed points. We also prove that the ordering of positive integers, determined by the coexistence of periods of endomorphisms of a tree T, is linear if and only if T is an interval