A remark on first integrals of vector fields

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André Belotto da Silva
Université de Paris, Institut de Mathématiques de Jussieu Paris Rive Gauche
Martin Klimeš
University of Zagreb. Faculty of Electrical Engineering and Computing
Julio Rebelo
Institut de Mathématiques de Toulouse
Helena Reis
Universidade do Porto. Centro de Matemática

We provide examples of vector fields on (C3 , 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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holomorphic vector field, first integral, formal power series, Stokes phenomena

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Belotto da Silva, André et al. «A remark on first integrals of vector fields». Publicacions Matemàtiques, 2024, vol.VOL 68, núm. 1, p. 103-9, http://raco.cat/index.php/PublicacionsMatematiques/article/view/422917.
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