Zero-Hopf polynomial centers of third-order differential equations
We study the 3-dimensional center problem at the zero-Hopf singularity in some families of polynomial vector fields arising from third-order polynomial differential equations. After proving some general properties we check that the quadratic family has no 3-dimensional centers. Later we characterize...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universitat de Lleida (UdL) |
| Repositorio: | Repositori Obert UdL |
| OAI Identifier: | oai:repositori.udl.cat:10459.1/58381 |
| Acceso en línea: | https://doi.org/10.1007/s10884-016-9558-y http://hdl.handle.net/10459.1/58381 |
| Access Level: | acceso abierto |
| Palabra clave: | Zero-Hopf singularity Three-dimensional vector fields Continua of periodic orbits Poincaré map |
| Sumario: | We study the 3-dimensional center problem at the zero-Hopf singularity in some families of polynomial vector fields arising from third-order polynomial differential equations. After proving some general properties we check that the quadratic family has no 3-dimensional centers. Later we characterize all the 3-dimensional centers in the cubic homogeneous family. Finally we give a partial classification of the 3-dimensional centers at just one singularity of the full cubic family and propose one open problem to close this classification. |
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