Estudo qualitativo de equações diferenciais binárias cúbicas

• Autor(a) principal: Maranhão Neto, Raimundo Cavalcante
• Data de Publicação: 2022
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• dARK ID: ark:/38995/0013000000b9g
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/12572
• topic: Equações diferencias ordinárias implícitas de primeira ordem; Lie-Cartan; Linhas de Laguerre; Binárias cúbicas; First order implicit ordinary differential equations; Lie-Cartan; Laguerre lines; Cubic binaries; CIENCIAS EXATAS E DA TERRA::MATEMATICA

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.