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| Home > Articles > Published articles > Global centres in a class of quintic polynomial differential systems |
(Universidade de São Paulo. Instituto de Ciências Matemáticas e de Computação) (Universitat Autònoma de Barcelona. Departament de Matemàtiques)| Date: | 2026 |
| Abstract: | 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. |
| Grants: | Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911 Generalitat de Catalunya 2021/SGR-00113 |
| Note: | Altres ajuts: Acadèmia de Ciències i Arts de Barcelona |
| Rights: | Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.  |
| Language: | Anglès |
| Document: | Article ; recerca ; Versió acceptada per publicar |
| Subject: | Centre ; Global centre ; Polynomial differential systems ; Lyapunov quantities ; Blow up ; Quintic polynomial |
| Published in: | Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Vol. 156, Num. 1 (February 2026) , p. 39-54, ISSN 1473-7124 |
Postprint 18 p, 308.1 KB |
