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Erschienen in: Journal of Dynamical and Control Systems 3/2019

12.03.2019

Analytic Classification of Foliations Induced by Germs of Holomorphic Vector Fields in \((\mathbb {C}^{n},0)\) with Non-isolated Singularities

verfasst von: L. Ortiz-Bobadilla, E. Rosales-González, S. M. Voronin

Erschienen in: Journal of Dynamical and Control Systems | Ausgabe 3/2019

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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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Metadaten
Titel
Analytic Classification of Foliations Induced by Germs of Holomorphic Vector Fields in with Non-isolated Singularities
verfasst von
L. Ortiz-Bobadilla
E. Rosales-González
S. M. Voronin
Publikationsdatum
12.03.2019
Verlag
Springer US
Erschienen in
Journal of Dynamical and Control Systems / Ausgabe 3/2019
Print ISSN: 1079-2724
Elektronische ISSN: 1573-8698
DOI
https://doi.org/10.1007/s10883-019-09436-7

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