Periodic orbits of maps of Y.

We introduce some notions that are useful for studying the behavior of periodic orbits of maps of one-dimensional spaces. We use them to characterize the set of periods of periodic orbits for continuous maps of Y = (z ∈ C: z3 ∈ [0, 1]) into itself having zero as a fixed point. We also obtain new proofs of some known results for maps of an interval into itself. © 1989 American Mathematical Society.