Let Y = (z∈C:z3∈[0, 1]) and let Y be the set of all continuous maps from Y into itself having 0 as a fixed point. We study the set of periods of maps from Y having all periodic orbits with a division. From this result and the results from Alsedà, Llibre, and Misiurewicz [Trans. Amer. Math. Soc., 313 (1989), 475-538] we obtain a generalization of the theorem about the characterization of the set of D-functions of minimal sets of interval mappings to maps from Y. © 1994 Academic Press, Inc.