Conservative surface homeomorphisms with finitely many periodic points
Abstract
The goal of the article is to characterize the conservative homeomorphisms of a closed orientable surface S of genus ≥2, that have finitely many periodic points. By conservative, we mean a map with no wandering point. As a particular case, when S is furnished with a symplectic form, we characterize the symplectic diffeomorphisms of S with finitely many periodic points.