Monodromic Nilpotent Singular Points with Odd Andreev Number and the Center Problem
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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.
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Qualitative Theory Of Dynamical Systems. Basel: Springer Basel Ag, v. 21, n. 4, 24 p., 2022.
