Periods of Morse-Smale diffeomorphisms on , , and .

We study the set of periods of the Morse-Smale diffeomorphisms on the -dimensional sphere , on products of two spheres of arbitrary dimension with , on the -dimensional complex projective space and on the -dimensional quaternion projective space . We classify the minimal sets of Lefschetz periods for such Morse-Smale diffeomorphisms. This characterization is done using the induced maps on the homology. The main tool used is the Lefschetz zeta function.