New families of global cubic centers
An equilibrium point p of a differential system in the plane R2 is a center if there exists a neighbourhood U of p such that U\{p} is filled with periodic orbits. A difficult classical problem in the qualitative theory of differential systems in the plane R2 is the problem of distinguishing between...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | Brasil |
| Institución: | Universidade Estadual Paulista (UNESP) |
| Repositorio: | Repositório Institucional da UNESP |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unesp.br:11449/302129 |
| Acceso en línea: | http://dx.doi.org/10.1007/s40863-024-00411-0 https://hdl.handle.net/11449/302129 |
| Access Level: | acceso abierto |
| Palabra clave: | Center Cubic polynomial differential systems Global center |
| Sumario: | An equilibrium point p of a differential system in the plane R2 is a center if there exists a neighbourhood U of p such that U\{p} is filled with periodic orbits. A difficult classical problem in the qualitative theory of differential systems in the plane R2 is the problem of distinguishing between a focus and a center. A global center is a center p such that R2\{p} is filled with periodic orbits. Another difficult problem in the qualitative theory of differential systems in R2 is to distinguish inside a family of centers the ones which are global. Lloyd, Pearson and Romanovsky characterized when the origin of coordinates is a center for the family of cubic polynomial differential systems x˙=y-Cx2+B+2Dxy+Cy2+Px3+Gx2y-H+3Pxy2+Ky3,y˙=-x+Dx2+E+2Cxy-Dy2-Kx3-H+3Px2y-Gxy2+Py3. Here we characterize when the origin of this family of differential system is a global center. |
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