Global centers of a class of cubic polynomial differential systems
A difficult classical problem in the qualitative theory of differential systems in the plane R is the center-focus problem, i.e. to distinguish between a focus and a center. Another difficult problem is to distinguish inside a family of centers the ones which are global. A global center is a center...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:303176 |
| Acceso en línea: | https://ddd.uab.cat/record/303176 https://dx.doi.org/urn:doi:10.1007/s12215-024-01034-2 |
| Access Level: | acceso abierto |
| Palabra clave: | Global centers Vertical blow-up Polynomial differential equations |
| Sumario: | A difficult classical problem in the qualitative theory of differential systems in the plane R is the center-focus problem, i.e. to distinguish between a focus and a center. Another difficult problem is to distinguish inside a family of centers the ones which are global. A global center is a center p such that R\{p} is filled with periodic orbits. In this paper we classify the global centers of the family of real polynomial differential systems of degree 3 that in complex notation write (Formula presented.) where w = x + iy and A ∈ C for k = 3, 4, 5, 6. |
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