Singularidades de Equações Diferenciais Implícitas

In this work we study implicit differential equations. Following the Thom tranversality theorem and the singularity theory we find an open and dense subset of this equation class that present only good singularity. This singularity are of six kind well folded saddle, well folded node, well folded fo...

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Detalles Bibliográficos
Autor: Oliveira, Francisco Vieira de
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2013
País:Brasil
Institución:Universidade Federal da Paraíba (UFPB)
Repositorio:Biblioteca Digital de Teses e Dissertações da UFPB
Idioma:portugués
OAI Identifier:oai:repositorio.ufpb.br:tede/7377
Acceso en línea:https://repositorio.ufpb.br/jspui/handle/tede/7377
Access Level:acceso abierto
Palabra clave:Equações diferenciais implicitas
Implicit diffrential equation
Forma normal
Equações diferenciais binárias
Transversalidade de Thom
Normal form
Binary diffrential equation
Thom transversality
CIENCIAS EXATAS E DA TERRA::MATEMATICA
Descripción
Sumario:In this work we study implicit differential equations. Following the Thom tranversality theorem and the singularity theory we find an open and dense subset of this equation class that present only good singularity. This singularity are of six kind well folded saddle, well folded node, well folded focus, elliptical gather, hyperbolic gather. Davydov,in [8] showed the normal forms of a IDE in the case of well folded saddle, well folded node, well folded focus. In the case of gathered singularities, Davydov showed that the normal forms of IDE contains functional moduli. For a special class of implicit differential equation, the binary differential equation (BDE), we study the normal forms in the case in that the discriminant is a Morse function.