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

Resultado de la investigación: Contribución a una revistaArtículo

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 originalInglés
PublicaciónJournal of Dynamical and Control Systems
DOI
EstadoPublicada - 1 ene 2019

Huella dactilar

Holomorphic Vector Field
Nonsingularity
Foliation
Singular Point
Linearization
Submanifolds
Codimension
Normalization
Modulus
Trivial
Eigenvalue
Zero

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title = "Analytic Classification of Foliations Induced by Germs of Holomorphic Vector Fields in (ℂ n , 0) with Non-isolated Singularities",
abstract = "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 Ast{\'e}risque. 1975;30:1–181).",
keywords = "Foliations, Holomorphic vector fields, Monodromy, Non-isolated singularities, Normal forms",
author = "{Ortiz Bobadilla}, Laura and {Rosales Gonzalez}, Ernesto and Voronin, {S. M.}",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/s10883-019-09436-7",
language = "Ingl{\'e}s",
journal = "Journal of Dynamical and Control Systems",
issn = "1079-2724",
publisher = "Springer New York",

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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

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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 -