PERIODIC POINTS OF SELF-MAPS OF PRODUCTS OF LENS SPACES L(3) x L(3)

Let f: M -> M be a self-map of a compact manifold and n is an element of N. The least number of n-periodic points in the smooth homotopy class of f may be smaller than in the continuous homotopy class. We ask: for which self-maps f: M -> M the two minima are the same, for each prescribed multiplicity? In the study of self-maps of tori and compact Lie groups a necessary condition appears. Here we give a criterion which helps to decide whether the necessary condition is also sufficient. We apply this result to show that for self-maps of the product of the lens space M = L(3) x L(3) the necessary condition is also sufficient.