Partially periodic point free self-maps on surfaces, graphs, wedge sums and products of spheres

Abstract

Let (X, f) be a topological dynamical system. We say that it is partially periodic point free up to period n, if f does not have periodic points of periods smaller than n + 1. When X is a compact connected surface, a connected compact graph, or S2m ∨ Sm ∨ · · · ∨ Sm, we give conditions on X, so that there exist partially periodic point free maps up to period n. We also introduce the notion of a Lefschetz partially periodic point free map up period n. This is a weaker concept than partially periodic point free up period n. We characterize the Lefschetz partially periodic point free self-maps for the manifolds Sn×k· · · ×Sn, Sn × Sm with n ̸= m, CPn, HPn and OPn.