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...

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Bibliographic Details
Author: Giné, Jaume
Format: article
Status:Published version
Publication Date:2024
Country:España
Institution:Universitat de Lleida (UdL)
Repository:Repositori Obert UdL
OAI Identifier:oai:repositori.udl.cat:10459.1/465862
Online Access:https://doi.org/10.1002/mma.10197
https://hdl.handle.net/10459.1/465862
Access Level:Open access
Keyword:Analytic integrability
Cherkas method
Decomposition in prime ideals
Nilpotent center problem
Polynomial differential systems
Takens normal form
Description
Summary: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.