| Full text | |
| Author(s): |
Pessoa, Claudio
;
Queiroz, Lucas
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Journal of Mathematical Analysis and Applications; v. 525, n. 1, p. 17-pg., 2023-03-02. |
| Abstract | |
Consider analytical three-dimensional differential systems having a singular point at the origin such that its linear part is y partial derivative(chi) - lambda z partial derivative(z) for some lambda not equal 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. (AU) | |
| FAPESP's process: | 19/10269-3 - Ergodic and qualitative theories of dynamical systems II |
| Grantee: | Claudio Aguinaldo Buzzi |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 19/13040-7 - Nilpotent centers on the center manifolds |
| Grantee: | Lucas Queiroz Arakaki |
| Support Opportunities: | Scholarships in Brazil - Doctorate |