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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

[en] COMPLEX ORDINARY DIFFERENTIAL EQUATIONS / [pt] EQUAÇÕES DIFERENCIAIS ORDINÁRIAS COMPLEXAS

GISELA DORNELLES MARINO 25 July 2007 (has links)
[pt] Neste texto estudamos diversos aspectos de singularidades de campos vetoriais holomorfos em dimensão 2. Discutimos detalhadamente o caso particular de uma singularidade sela-nó e o papel desempenhado pelas normalizações setoriais. Isto nos conduz à classificação analítica de difeomorfismos tangentes à identidade. seguir abordamos o Teorema de Seidenberg, tratando da redução de singularidades degeneradas em singularidades simples, através do procedimento de blow-up. Por fim, estudamos a demonstração do Teorema de Mattei-Moussu, acerca da existência de integrais primeiras para folheações holomorfas. / [en] In the present text, we study the different aspects of singularities of holomorphic vector fields in dimension 2. We discuss in detail the particular case of a saddle-node singularity and the role of the sectorial normalizations. This leads us to the analytic classiffication of diffeomorphisms which are tangent to the identity. Next, we approach the Seidenberg Theorem, dealing with the reduction of degenerated singularities into simple ones, by means of the blow-up procedure. Finally, we study the proof of the well-known Mattei-Moussu Theorem concerning the existence of first integrals to holomorphic foliations.

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