Estudo qualitativo de equações diferenciais binárias cúbicas
Saved in:
| Main Author: | |
|---|---|
| Publication Date: | 2022 |
| Format: | Doctoral thesis |
| Language: | por |
| Source: | Repositório Institucional da UFG |
| Download full: | http://repositorio.bc.ufg.br/tede/handle/tede/12572 |
Summary: | 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. |
Similar Items: Estudo qualitativo de equações diferenciais binárias cúbicas
- Equações diferenciais ordinárias na modelagem e solução de problemas de engenharia
- Geometria de Laguerre e representação para superfícies mínimas generalizadas de Laguerre
- Sobre hipersuperfícies isotrópicas de Laguerre
- Geometria de Laguerre e hipersuperficies de Dupin com curvatura de Laguerre constante em Rn+1
- On the crossing limit cycles for piecewise linear differential systems on the plane
- Equações diferenciais ordinárias lineares com coeficientes constantes e derivação da equação característica