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

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 S2m V Sm V...V 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 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, with n ≠ m, CPn, ℍPn and OPn. © 2013 Copyright Taylor and Francis Group, LLC.