### Resumen

We consider germs of holomorphic vector fields in (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).

Idioma original | Inglés |
---|---|

Publicación | Journal of Dynamical and Control Systems |

DOI | |

Estado | Publicada - 1 ene 2019 |

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**
Analytic Classification of Foliations Induced by Germs of Holomorphic Vector Fields in (ℂ
^{n}
, 0) with Non-isolated Singularities
.** / Ortiz Bobadilla, Laura; Rosales Gonzalez, Ernesto; Voronin, S. M.

Resultado de la investigación: Contribución a una revista › Artículo

TY - JOUR

T1 - Analytic Classification of Foliations Induced by Germs of Holomorphic Vector Fields in (ℂ n , 0) with Non-isolated Singularities

AU - Ortiz Bobadilla, Laura

AU - Rosales Gonzalez, Ernesto

AU - Voronin, S. M.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We consider germs of holomorphic vector fields in (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).

AB - We consider germs of holomorphic vector fields in (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).

KW - Foliations

KW - Holomorphic vector fields

KW - Monodromy

KW - Non-isolated singularities

KW - Normal forms

UR - http://www.scopus.com/inward/record.url?scp=85063001531&partnerID=8YFLogxK

U2 - 10.1007/s10883-019-09436-7

DO - 10.1007/s10883-019-09436-7

M3 - Artículo

AN - SCOPUS:85063001531

JO - Journal of Dynamical and Control Systems

JF - Journal of Dynamical and Control Systems

SN - 1079-2724

ER -