Estudo qualitativo de equações diferenciais binárias cúbicas
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Data
2022-12-05
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Universidade Federal de Goiás
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.
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Citação
MARANHÃO NETO, R. C. Estudo qualitativo de equações diferenciais binárias cúbicas. 2022. 147 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2022.