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Anais da Academia Brasileira de Ciências

versão impressa ISSN 0001-3765versão On-line ISSN 1678-2690

Resumo

MOVASATI, HOSSEIN. On deformation of foliations with a center in the projective space. An. Acad. Bras. Ciênc. [online]. 2001, vol.73, n.2, pp.191-196. ISSN 0001-3765.  http://dx.doi.org/10.1590/S0001-37652001000200004.

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 ft.gif (149 bytes) be a deformation of in the space of foliations of degree deg() such that its unique deformed singularity zt.gif (118 bytes) near z persists in being a center. We will prove that the foliation ft.gif (149 bytes) 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.

Palavras-chave : Holomorphic foliation; limit cycle; center singularity.

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