Authors

Citation

H. Movasati, On deformation of foliations with a center in the projective space, AN AC BRASI, 73(2), 2001, pp. 191-196

Citations number

5

Language

INGLESE

art.tipo

Article

Categorie Soggetti

Multidisciplinary

Journal title

ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS

ISSN journal

0001-3765
â†’ ACNP

Volume

73

Issue

2

Year of publication

2001

Pages

191 - 196

Database

ISI

SICI code

0001-3765(200106)73:2<191:ODOFWA>2.0.ZU;2-A

Abstract

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