On Deformation of Foliations with a Center in the Projective Space
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| Format: | Artículo científico |
| Langue: | en |
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Academia Brasileira de Ciências
2001
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| _version_ | 1876462936389582848 |
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| author | Hossein Movasati |
| author_facet | Hossein Movasati |
| contents | On Deformation of Foliations with a Center in the Projective Space Hossein Movasati Multidisciplinaria (Ciencias Naturales y Exactas) limit cycle center singularity Holomorphic foliation Let F be a foliation in the projective space of dimension two with a first integral of the type FpGq ,where F and G are two polynomials on an affine coordinate, deg(F)deg(G) = qp and g.c.d.(p, q) = 1.Let z be a nondegenerate critical point of FpGq , which is a center singularity of F, and Ft bea deformation of F in the space of foliations of degree deg(F) such that its unique deformedsingularity zt near z persists in being a center. We will prove that the foliation Ft has a firstintegral of the same type of F. Using the arguments of the proof of this result we will give a lowerbound for the maximum number of limit cycles of real polynomial differential equations of a fixeddegree in the real plane. 2001 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32773204 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.2 Vol.73 |
| format | Artículo científico |
| id | redalyc_32773204 |
| institution | Redalyc |
| language | en |
| publishDate | 2001 |
| publisher | Academia Brasileira de Ciências |
| spellingShingle | On Deformation of Foliations with a Center in the Projective Space Hossein Movasati Multidisciplinaria (Ciencias Naturales y Exactas) limit cycle center singularity Holomorphic foliation On Deformation of Foliations with a Center in the Projective Space Hossein Movasati Multidisciplinaria (Ciencias Naturales y Exactas) limit cycle center singularity Holomorphic foliation Let F be a foliation in the projective space of dimension two with a first integral of the type FpGq ,where F and G are two polynomials on an affine coordinate, deg(F)deg(G) = qp and g.c.d.(p, q) = 1.Let z be a nondegenerate critical point of FpGq , which is a center singularity of F, and Ft bea deformation of F in the space of foliations of degree deg(F) such that its unique deformedsingularity zt near z persists in being a center. We will prove that the foliation Ft has a firstintegral of the same type of F. Using the arguments of the proof of this result we will give a lowerbound for the maximum number of limit cycles of real polynomial differential equations of a fixeddegree in the real plane. 2001 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32773204 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.2 Vol.73 |
| title | On Deformation of Foliations with a Center in the Projective Space |
| topic | Multidisciplinaria (Ciencias Naturales y Exactas) limit cycle center singularity Holomorphic foliation |
| url | https://www.redalyc.org/articulo.oa?id=32773204 |