About periodic points of conservative surface diffeomorphisms

As explained by Poincaré, periodic points are of high importance in the study of the dynamics of volume preserving diffeomorphisms on a manifold M. There is still a lot of open questions concerning periodic points, even in the case where M is two dimensional. We will report on some recent progress about periodic points of area preserving diffeomorphisms of surface and more generally of homeomorphisms with no wandering points.