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Article Dans Une Revue Moscow Mathematical Journal Année : 2021

Integrable deformations of foliations: a generalization of Ilyashenko's result

Résumé

We study analytic deformations of holomorphic differential 1-forms. The initial 1-form is exact homogeneous and the deformation is by polynomial integrable 1-forms. We investigate under which conditions the elements of the deformation are still exact or, more generally, exhibit a first integral. Our results are related to natural extensions of classical results of Ilyashenko on limit cycles of perturbations of hamiltonian systems in two complex variables.

Dates et versions

hal-01937834 , version 1 (28-11-2018)

Identifiants

Citer

Dominique Cerveau, Bruno Scardua. Integrable deformations of foliations: a generalization of Ilyashenko's result. Moscow Mathematical Journal, 2021, 21 (2), pp.271-286. ⟨10.17323/1609-4514-2021-21-2-271-286⟩. ⟨hal-01937834⟩
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