Centers for the Kukles homogeneous systems with odd degree
For the polynomial differential system x ̇ = -y, y ̇ = x Q n (x, y), where Q n (x, y) is a homogeneous polynomial of degree n there are the following two conjectures raised in 1999. (1) Is it true that the previous system for n 2 has a center at the origin if and only if its vector field is symmetri...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:145329 |
| Acceso en línea: | https://ddd.uab.cat/record/145329 https://dx.doi.org/urn:doi:10.1112/blms/bdv005 |
| Access Level: | acceso abierto |
| Palabra clave: | Bautin method Complex center-focus problem Lyapunov constants |
| Sumario: | For the polynomial differential system x ̇ = -y, y ̇ = x Q n (x, y), where Q n (x, y) is a homogeneous polynomial of degree n there are the following two conjectures raised in 1999. (1) Is it true that the previous system for n 2 has a center at the origin if and only if its vector field is symmetric about one of the coordinate axes? (2) Is it true that the origin is an isochronous center of the previous system with the exception of the linear center only if the system has even degree? We prove both conjectures for all n odd. |
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