A remark on first integrals of vector fields

We provide examples of vector fields on \((\mathbb{C}^3, 0)\) admitting a formal first integral but no holomorphic first integral. These examples are related to a question raised by D. Cerveau and motivated by the celebrated theorems of Malgrange and Mattei-Moussu.

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Bibliographic Details
Published in:arXiv.org 2021-10
Main Authors: André Belotto da Silva, Klimes, Martin, Rebelo, Julio C, Reis, Helena
Format: Article
Language:English
Subjects:
Fields (mathematics)
Online Access:Get full text
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Summary:We provide examples of vector fields on \((\mathbb{C}^3, 0)\) admitting a formal first integral but no holomorphic first integral. These examples are related to a question raised by D. Cerveau and motivated by the celebrated theorems of Malgrange and Mattei-Moussu.
ISSN:2331-8422