On deformation of foliations with a center in the projective space

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 → 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.