Detalhes bibliográficos
| Ano de defesa: |
2022 |
| Autor(a) principal: |
Maranhão Neto, Raimundo Cavalcante
 |
| Orientador(a): |
Garcia, Ronaldo Alves
|
| Banca de defesa: |
Garcia, Ronaldo Alves,
Freitas, Bruno Rodrigues de,
Martins, Luciana de Fátima,
Euzébio, Rodrigo Donizete,
Buzzi, Claudio Aguinaldo |
| Tipo de documento: |
Tese
|
| Tipo de acesso: |
Acesso aberto |
| Idioma: |
por |
| Instituição de defesa: |
Universidade Federal de Goiás
|
| Programa de Pós-Graduação: |
Programa de Pós-graduação em Matemática (IME)
|
| Departamento: |
Instituto de Matemática e Estatística - IME (RMG)
|
| País: |
Brasil
|
| Palavras-chave em Português: |
|
| Palavras-chave em Inglês: |
|
| Área do conhecimento CNPq: |
|
| Link de acesso: |
http://repositorio.bc.ufg.br/tede/handle/tede/12572
|
Resumo: |
In this work we present a qualitative study for two classes of differential equations. The first of these is of the form Im[(a + i b)(du + i dv)3 ] = 0 (0-1) where a, b : R 2 → R are functions of class C∞ and the second is from the implicit differential equation of the Laguerre lines of a surface of class C6 . This second class, as proved in [5], has the shape A3(u, v) dv3 + 3 A2(u, v) dv2 du + 3 A1(u, v) dv du2 + A0(u, v) du3 = 0. With regard to equations of the form (0-2), we perform a local study, express the derivative of the application of the first return, we classify the singularities at infinity and present a global result for the case where a and b are polynomials of degree one. For the differential equation of the Laguerre lines, we studied the qualitative behavior close to the discriminant curve, we made a partial study of the singularities, we presented an expression for the derivative of the application of the first return, we carried out a study of structural stability and we studied the particular cases for surfaces of rotation , ruled surfaces and quadric surfaces. |
