Monodromic Nilpotent Singular Points with Odd Andreev Number and the Center Problem - Pessoa, Claudio [UNESP]; Queiroz, Lucas [UNESP] (Springer, 2022)
Given 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.
Keywords: Monodromy; Nilpotent singular points; Center Problem