On deformation of foliations with a center in the projective space

Anais da Academia Brasileira de Ciências

Hossein Movasati¹ 

[1] ,Instituto de Matemática Pura e AplicadaRio de Janeiro RJ ,Brazil

关键词: Holomorphic foliation;    limit cycle;    center singularity;    folheação holomórfica;    ciclo limite;    singularidade do tipo centro;   

DOI  :  10.1590/S0001-37652001000200004

来源: SciELO

【 摘 要 】

Let be a foliation in the projective space of dimension two with a first integral of the type , where F and G are two polynomials on an affine coordinate, = and g.c.d.(p, q) = 1. Let z be a nondegenerate critical point of , which is a center singularity of , and be a deformation of in the space of foliations of degree deg() such that its unique deformed singularity near z persists in being a center. We will prove that the foliation has a first integral of the same type of . Using the arguments of the proof of this result we will give a lower bound for the maximum number of limit cycles of real polynomial differential equations of a fixed degree in the real plane.

【 授权许可】

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