A method for characterizing nilpotent centers

To characterize when a nilpotent singular point of an analytic differential system is a center is of particular interest, first for the problem of distinguishing between a focus and a center, and second for studying the bifurcation of limit cycles from it or from its period annulus. We provide necessary conditions for detecting nilpotent centers based on recent developments. Moreover we survey the last results on this problem and illustrate our approach by means of examples.