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arXiv · 2110.13072

A remark on first integrals of vector fields

André Belotto da Silva·Martin Klimes·Julio C. 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 Klimes, Julio C. Rebelo, Helena Reis. 2021-10-25. A remark on first integrals of vector fields. https://arxiv.org/abs/2110.13072

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