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 \(n=3\).
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Acknowledgements
The first author is partially supported by São Paulo Research Foundation (FAPESP) grants 19/10269-3 and 18/19726-5. The second author is supported by São Paulo Research Foundation (FAPESP) grant 19/13040-7.
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Pessoa, C., Queiroz, L. Monodromic Nilpotent Singular Points with Odd Andreev Number and the Center Problem. Qual. Theory Dyn. Syst. 21, 109 (2022). https://doi.org/10.1007/s12346-022-00638-2
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DOI: https://doi.org/10.1007/s12346-022-00638-2