on deformation of foliations with a center in the projective space
Clicks: 11
ID: 257085
2001
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Abstract
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.
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.| Reference Key |
hossein2001anaison
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|---|---|
| Authors | ;MOVASATI HOSSEIN |
| Journal | hypertension (dallas, tex : 1979) |
| Year | 2001 |
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