Nilpotent centres via inverse integrating factors

Abstract

In this paper we are interested in the nilpotent center problem of planar analytic monodromic vector fields. It is known that the formal integrability is not enough to characterize such centers. More general objects are considered as the formal inverse integrating factors. However the existence of a formal inverse integrating factor is not sufficient to describe all the nilpotent centers. For the family studied in this paper it is enough.