Center conditions: Rigidity of logarithmic differential equations
| dc.creator | Movasati, Hossein | |
| dc.date | 2002-05-07 | |
| dc.date | 2004-07-05 | |
| dc.date.accessioned | 2026-07-07T04:48:19Z | |
| dc.date.available | 2026-07-07T04:48:19Z | |
| dc.description | In this paper we prove that any degree $d$ deformation of a generic logarithmic polynomial differential equation with a persistent center must be logarithmic again. This is a generalization of Ilyashenko's result on Hamiltonian differential equations. The main tools are Picard-Lefschetz theory of a polynomial with complex coefficients in two variables, specially the Gusein-Zade/A'Campo's theorem on calculating the Dynkin diagram of the polynomial, and the action of Gauss-Manin connection on the so called Brieskorn lattice/Petrov module of the polynomial. Some applications on the cyclicity of cycles and the Bautin ideals will be given. | |
| dc.description | 20 pages | |
| dc.identifier | https://arxiv.org/abs/math/0205068 | |
| dc.identifier | http://arxiv.org/abs/math/0205068 | |
| dc.identifier | Journal of Differential equations, 197 (2004), 197-217 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63999 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 32L30; 14D05 | |
| dc.title | Center conditions: Rigidity of logarithmic differential equations | |
| dc.type | text |