A REMARK ON FIRST INTEGRALS OF VECTOR FIELDS

André Belotto da Silva; Martin Klimeš; Julio Rebelo; Helena Reis

doi:10.5565/PUBLMAT6812405

2024 A REMARK ON FIRST INTEGRALS OF VECTOR FIELDS

André Belotto da Silva, Martin Klimeš, Julio Rebelo, Helena Reis

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Abstract

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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André Belotto da Silva. Martin Klimeš. Julio Rebelo. Helena Reis. "A REMARK ON FIRST INTEGRALS OF VECTOR FIELDS." Publ. Mat. 68 (1) 103 - 109, 2024. https://doi.org/10.5565/PUBLMAT6812405

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Received: 29 October 2021; Accepted: 15 June 2022; Published: 2024

First available in Project Euclid: 25 December 2023

MathSciNet: MR4682725

Digital Object Identifier: 10.5565/PUBLMAT6812405

Subjects:

Primary: 32S65

Secondary: 32M25

Keywords: first integral , formal power series , holomorphic vector field , Stokes phenomena

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