Analytic integrability of certain resonant saddle
We provide sufficient conditions of analytic integrability for a family of planar differential system with a p : −q resonant saddle at the origin. The conditions are then shown to be necessary in several finite dimensional families where the calculations can be performed explicitly. It is conjecture...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10459.1/72475 |
| Acceso en línea: | https://doi.org/10.1016/j.chaos.2021.110821 http://hdl.handle.net/10459.1/72475 |
| Access Level: | acceso abierto |
| Palabra clave: | Blow-up Resonant saddle Saddle constants Formal first integral |
| Sumario: | We provide sufficient conditions of analytic integrability for a family of planar differential system with a p : −q resonant saddle at the origin. The conditions are then shown to be necessary in several finite dimensional families where the calculations can be performed explicitly. It is conjectured that the conditions are in fact complete for all families. Though the form of the equations is quite simple, their study merits further attention as they exhibit an interesting dichotomy between finite and arbitrary dimensional components of the center variety. |
|---|