Periodic points of self-maps of products of lens spaces L(3)× L(3) - Jezierski, Jerzy (Topological Methods in Nonlinear Analysis, 2023)
Let fM→ M be a self-map of a compact manifold and nN. 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 fM→ 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.