Stability condition for nilpotent singularities by its complex separatrices

This work is focused in the center problem for nilpotent singularities of differential systems in the plane. Although there are involved methods to approach the center problem in this work, we present a new stability criteria based on the existence of the complex separatrices passing through the sin...

Descripción completa

Detalles Bibliográficos
Autor: Giné, Jaume
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
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:10459.1/465862
Acceso en línea:https://doi.org/10.1002/mma.10197
https://hdl.handle.net/10459.1/465862
Access Level:acceso abierto
Palabra clave:Analytic integrability
Cherkas method
Decomposition in prime ideals
Nilpotent center problem
Polynomial differential systems
Takens normal form
Descripción
Sumario:This work is focused in the center problem for nilpotent singularities of differential systems in the plane. Although there are involved methods to approach the center problem in this work, we present a new stability criteria based on the existence of the complex separatrices passing through the singular point, and independent of the normal form. The algebraic method needs only the computation of such complex separatrices up to certain order, which can be done with a computer algebra package.