Pessoa, Claudio [UNESP]Queiroz, Lucas [UNESP]2022-11-302022-11-302022-12-01Qualitative Theory Of Dynamical Systems. Basel: Springer Basel Ag, v. 21, n. 4, 24 p., 2022.1575-5460http://hdl.handle.net/11449/237645Given a nilpotent singular point of a planar vector field, its monodromy is associated with its Andreev number n. The parity of n determines whether the existence of an inverse integrating factor implies that the singular point is a nilpotent center. For n odd, this is not always true. We give a characterization for a family of systems having Andreev number n such that the center problem cannot be solved by the inverse integrating factor method. Moreover, we study general properties of this family, determining necessary center conditions for every n and solving the center problem in the case n = 3.24engMonodromyNilpotent singular pointsCenter ProblemArtigo10.1007/s12346-022-00638-2WOS:000834818300001