Algorithmic Derivation of 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 after for studying the bifurcation of limit cycles from it or from its period annulus. We give an effective algorithm in the search of necessary conditions for detecting nilpotent centers based in recent developments. Moreover we survey the last results on this problem and illustrate our approach by means of examples.