Singularidades de Equações Diferenciais Implícitas

• Ano de defesa: 2013
• Autor(a) principal: Oliveira, Francisco Vieira de
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraí­ba; BR; Matemática; Programa de Pós-Graduação em Matemática; UFPB
• Palavras-chave em Português: 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
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/7377

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.