Periodic points of self-maps of products of lens spaces $L(3)× L(3)$ - Jezierski, Jerzy (Topological Methods in Nonlinear Analysis, 2023)
Let $f\colon M→ M$ be a self-map of a compact manifold and $n\in \mathbb{N}$.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$f\colon M→ M$ 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 $M=L(3)× L(3)$ the necessary condition is also sufficient.