On integral conditions for the existence of first integrals for analytic deformations of complex saddle singularities

DOI10.1007/s10883-022-09612-2arXiv2106.09172MaRDI QIDQ6145730

Víctor León, Bruno C. Azevedo Scárdua

Publication date: 9 January 2024

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.09172

zbMATH Keywords

foliationdeformationfirst integralintegrable formcenter singularity

Mathematics Subject Classification ID

Singularities of holomorphic vector fields and foliations (32S65) Foliations in differential topology; geometric theory (57R30) Complex vector fields, holomorphic foliations, (mathbb{C})-actions (32M25) Dynamical aspects of holomorphic foliations and vector fields (37F75)

Cites Work

• On a generalization of de Rham lemma
• Frobenius avec singularites. I: Codimension un
• Frobenius avec singularites. II: Le cas général
• Theory of Stein spaces. Transl. from the German by Alan Huckleberry
• Classification analytique des équations différentielles non linéaires résonnantes du premier ordre
• Holonomie et intégrales premières
• Quelques calculs de cohomologie relative
• Deformations of holomorphic foliations having a meromorphic first integral.
• Analytic deformations of pencils and integrable one-forms having a first integral
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