Periods of Morse–Smale diffeomorphisms on $${\mathbb {S}}^n$$, $${\mathbb {S}}^m \times {\mathbb {S}}^n$$, $${\mathbb {C}}{\mathbf{P }}^n$$ and $${\mathbb {H}}{\mathbf{P }}^n$$

We study the set of periods Morse–Smale diffeomorphisms on n-dimensional sphere $${\mathbb {S}}^n$$ , products two spheres arbitrary dimension {S}}^m \times {\mathbb with $$m \ne n$$ complex projective space {C}}{\mathbf{P }}^n$$ and quaternion {H}}{\mathbf{P . classify minimal sets Lefschetz for such diffeomorphisms. This characterization is done using induced maps homology. The main tool used zeta function.