Integrable deformations of foliations: a generalization of Ilyashenko's result
Algebraic Geometry
2018-11-13 v1 Complex Variables
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.
Keywords
Cite
@article{arxiv.1811.04222,
title = {Integrable deformations of foliations: a generalization of Ilyashenko's result},
author = {Dominique Cerveau and Bruno Scárdua},
journal= {arXiv preprint arXiv:1811.04222},
year = {2018}
}