The center problem for a family of systems of differential equations having a nilpotent singular point
We study the analytic system of differential equations in the plane(over(x, ̇), over(y, ̇))t = underover(∑, i = 0, ∞) Fq - p + 2 i s, where p, q ∈ N, p ≤ q, s = (n + 1) p - q > 0, n ∈ N, and Fi = (Pi, Qi)t are quasi-homogeneous vector fields of type t = (p, q) and degree i, with Fq - p = (y,...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2008 |
| País: | España |
| Institución: | Universidad de Huelva (UHU) |
| Repositorio: | Arias Montano. Repositorio Institucional de la Universidad de Huelva |
| Idioma: | inglés |
| OAI Identifier: | oai:ariasmontano.uhu.es:10272/25434 |
| Acceso en línea: | https://hdl.handle.net/10272/25434 |
| Access Level: | acceso abierto |
| Palabra clave: | Centers Nilpotent and monodromic singular point Lyapunov function 12 Matemáticas |
| Sumario: | We study the analytic system of differential equations in the plane(over(x, ̇), over(y, ̇))t = underover(∑, i = 0, ∞) Fq - p + 2 i s, where p, q ∈ N, p ≤ q, s = (n + 1) p - q > 0, n ∈ N, and Fi = (Pi, Qi)t are quasi-homogeneous vector fields of type t = (p, q) and degree i, with Fq - p = (y, 0)t and Qq - p + 2 s (1, 0) < 0. The origin of this system is a nilpotent and monodromic isolated singular point. We prove for this system the existence of a Lyapunov function and we solve theoretically the center problem for such system. Finally, as an application of the theoretical procedure, we characterize the centers of several subfamilies |
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