Perturbations of C1-diffeomorphisms and dynamics of generic conservative diffeomorphisms of surface

In the first part of this text we give a survey of the properties satisfied by the C1-generic conservative diffeomorphisms of compact surfaces. The main result that we will discuss is that a C1-generic conservative diffeomorphism of a connected compact surface is transitive. It is obtain as a consequence of a connecting lemma for pseudo-orbits. In the last parts we expose some recent developments of the C1-perturbation technics and the proof of this connecting lemma. We are not aimed to deal with technicalities nor to give the finest availab