We shall recall briefly how can be the local phase portraits of the equilibrium points of an analytic differential system in the plane,and we shall put our attention in the centers.First in the kind of integrability of the different types of centers,and after in the focus–center problem,i.e.how to distinguish a center from a focus.This is a difficult problem which is not completely solved.We shall provide some new results using the divergence of the differential system.