The Sarkovskii order for periodic continua II

In this paper it is shown that the existence of three maximal proper periodic continua for a map of a hereditarily decomposable chainable continuum onto itself implies the existence of a maximal proper periodic continuum with odd period greater than one. Hence, while the periods of such continua do follow the Sarkovskii order apart from the case in which the ambient space is the union of two maximal proper periodic continua with period two, for any nondegenerate terminal segment of the Sarkovskii order that fails to contain an odd integer greater than one, there does not exist a map of a hereditarily decomposable chainable continuum onto itself for which the set of all periods of such continua is the prescribed terminal segment. It is also shown that, for any terminal segment of the Sarkovskii order that does contain an odd integer greater than one, there is a map of [ 0 , 1 ] onto itself for which the set of all periods of such continua is the prescribed terminal segment.