Periodic Points of

In this paper we study the set of periods of holomorphic maps on compact manifolds, using the periodic Lefschetz numbers introduced in D] and Ll], which can be computed from the homology class of the map. We show that these numbers contain information about the existence of periodic points of a given period and, if we assume the map to be transversal then they give us the exact number of such periodic orbits. We apply this result to the complex projective space of dimension n and to some special type of Hopf surfaces, partially characterizing their set of periods. In the rst case we also show that any holomorphic map of C P (n) of degree greater than one has innnitely many distinct periodic orbits, hence generalizing a theorem of FS]. We then characterize the set of periods of a holomorphic map on the Riemann sphere, hence giving an alternative proof of Baker's theorem in Ba].