Abstract

We are interested in fine structures of periodic orbits of area-preserving diffeomorphisms on Annulus. By considering the open book decomposition of a three dimensional manifold, we can relate the dynamics of certain flows on the manifold and the dynamics of area-preserving diffeomorphisms of surfaces. Recently, Hutchings and Weiler using information of Reeb flows on 3-dimensional contact manifolds, coming from ECH theory, obtain results about area-preserving diffeomorphisms of surfaces. We want to give further analysis to this results and obtain a more intrinsic result which contains all the situation.