On Deformation of Foliations with a Center in the Projective Space

Hossein Movasati

Keywords: Holomorphic foliation - holonomy - limit cycle - Lefschetz pencil - vanishing cycle - monodromy

Under some generic conditions on a foliation with a first integral of type F^p/G^q in the projective space of dimension two, we prove that the persistence of a center singularity after deformation of this foliation implies that the deformed foliation has a first integral of the same type as of the original foliation. With this we identify some irreducible components of the space of foliations with a center singularity and give some applications in the number of limit cycles of a real differential equation in the plane.

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