Desingularization of Nilpotent Singularities in Families of Planar Vector Fields

Proves a desingularization theorem for analytic families of two-dimensional vector fields, under the hypothesis that all its singularities have a non-vanishing first jet.

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This work aims to prove a desingularization theorem for analytic families of two-dimensional vector fields, under the hypothesis that all its singularities have a non-vanishing first jet. Application to problems of singular perturbations and finite cyclicity are discussed in the last chapter.