Global centres in a class of quintic polynomial differential systems
A centre of a differential system in the plane R2 is an equilibrium point p having a neighbourhood U such that U \ {p} is filled with periodic orbits. A centre p is global when R2 \ {p} is filled with periodic orbits. In general, it is a difficult problem to distinguish the centres from the foci for...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2026 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:325994 |
| Acceso en línea: | https://ddd.uab.cat/record/325994 https://dx.doi.org/urn:doi:10.1017/prm.2024.43 |
| Access Level: | acceso embargado |
| Palabra clave: | Centre Global centre Polynomial differential systems Lyapunov quantities Blow up Quintic polynomial |
| Sumario: | A centre of a differential system in the plane R2 is an equilibrium point p having a neighbourhood U such that U \ {p} is filled with periodic orbits. A centre p is global when R2 \ {p} is filled with periodic orbits. In general, it is a difficult problem to distinguish the centres from the foci for a given class of differential systems, and also it is difficult to distinguish the global centres inside the centres. The goal of this paper is to classify the centres and the global centres of the following class of quintic polynomial differential systems x˙=y,y˙=-x+a05y5+a14xy4+a23x2y3+a32x3y2+a41x4y+a50x5, in the plane R2. |
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