On the Lefschetz zeta function and the minimal sets of Lefschetz periods for Morse–Smale diffeomorphisms on products of ℓ-spheres

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

“…Indeed, for 1/(1 − t) 2 and (1 + t)/(1 − t), we have MPer L (f ) = {1}, because any other expression of the same Lefschetz zeta function as a product of terms the form (1 ± t p ) ±1 would provide at least the period 1.…”

“…Without trying to be exhaustive, see for instance [5,19,[22][23][24]. This interest continues during this first part of the twenty-first century, see for example [2,3,9,10,[15][16][17][18].…”

“…The set of periods for Morse-Smale diffeomorphisms on a product of any number of spheres of the same dimension has been studied in [2]. For the particular case of S n , we give more detailed results considering the orientation of the diffeomorphisms.…”

On topological entropy, Lefschetz numbers and Lefschetz zeta functions

“…As in the case of the n-dimensional torus if the eigenvalues of f * ℓ are root of unity then the Lefschetz zeta function of f is of the form (cf. [4]):…”

A Note on the Periodic Structure of Transversal Maps on the Torus and Products of Spheres

“…, and s i ≥ 1. It would quite interesting to achieve this goal We recall that in the particular case of X = X(n, s) for some n ≥ 1 and s > 1, the study of the minimal sets Lefschetz periods and the computation of the Lefschetz zeta function for quasi-unipotent maps was done in [3]. In the particular situation of the torus, i.e.…”