Abstract

Let (X, f) be a topological discrete 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 S-2m boolean OR S-m boolean OR ... boolean OR S-m, 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 to period n. This is a weaker concept than partially periodic point free up to period n. We characterize the Lefschetz partially periodic point free self-maps for the manifolds S-n x ...(k) x S-n, S-n x S-m with n not equal m, CPn, HPn and OPn.