Nilpotent centers from analytical systems on center manifolds
Consider analytical three-dimensional differential systems having a singular point at the origin such that its linear part is y∂x−λz∂z for some λ≠0. The restriction of such systems to a Center Manifold has a nilpotent singular point at the origin. We prove that if the restricted system is analytic a...
| Authors: | , |
|---|---|
| Format: | article |
| Status: | Published version |
| Publication Date: | 2023 |
| Country: | Brasil |
| Institution: | Universidade Estadual Paulista (UNESP) |
| Repository: | Repositório Institucional da UNESP |
| Language: | English |
| OAI Identifier: | oai:repositorio.unesp.br:11449/246980 |
| Online Access: | http://dx.doi.org/10.1016/j.jmaa.2023.127120 http://hdl.handle.net/11449/246980 |
| Access Level: | Open access |
| Keyword: | Center problem Monodromy Nilpotent singular points |
| Summary: | Consider analytical three-dimensional differential systems having a singular point at the origin such that its linear part is y∂x−λz∂z for some λ≠0. The restriction of such systems to a Center Manifold has a nilpotent singular point at the origin. We prove that if the restricted system is analytic and has a nilpotent center at the origin, with Andreev number 2, then the three-dimensional system admits a formal inverse Jacobi multiplier. We also prove that nilpotent centers of three-dimensional systems, on analytic center manifolds, are limits of Hopf-type centers. We use these results to solve the center problem for some three-dimensional systems without restricting the system to a parametrization of the center manifold. |
|---|