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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| 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 |
| 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. |
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