Abstract
We consider germs of holomorphic vector fields in \((\mathbb {C}^{n},0)\), n ≥ 3, with non-isolated singularities. We assume that the set of singular points forms a submanifold of codimension 2, and the sum of the nonzero eigenvalues of the linearization of the germs at each singular point is zero. We give the orbital analytic classification of generic germs of such type. It happens that, unlike the formal classification (which is trivial), the analytic one has functional moduli. The same result is obtained in the real-analytic case (the smooth normalization was obtained earlier in Roussarie Astérisque. 1975;30:1–181).
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We deeply thank the referee for his thoughtful comments and suggestions.
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This work was supported by UNAM-PAPIIT IN106217, CONACyT 219722, and RFBR 16-01-00766.
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Ortiz-Bobadilla, L., Rosales-González, E. & Voronin, S.M. Analytic Classification of Foliations Induced by Germs of Holomorphic Vector Fields in \((\mathbb {C}^{n},0)\) with Non-isolated Singularities. J Dyn Control Syst 25, 491–516 (2019). https://doi.org/10.1007/s10883-019-09436-7
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DOI: https://doi.org/10.1007/s10883-019-09436-7