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arXiv · 1811.04222

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

Dominique Cerveau·Bruno Scárdua
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Abstract

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.

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Dominique Cerveau, Bruno Scárdua. 2018-11-10. Integrable deformations of foliations: a generalization of Ilyashenko's result. https://arxiv.org/abs/1811.04222

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