Monodromic nilpotent singular points with odd Andreev number and the center problem

DOI10.1007/S12346-022-00638-2arXiv2106.05090WikidataQ114220808 ScholiaQ114220808MaRDI QIDQ6369873

Lucas Queiroz, Claudio Pessoa

Publication date: 9 June 2021

Abstract: 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 $n=3$.

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

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