Center conditions: Rigidity of logarithmic differential equations

dc.creatorMovasati, Hossein
dc.date2002-05-07
dc.date2004-07-05
dc.date.accessioned2026-07-07T04:48:19Z
dc.date.available2026-07-07T04:48:19Z
dc.descriptionIn 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.description20 pages
dc.identifierhttps://arxiv.org/abs/math/0205068
dc.identifierhttp://arxiv.org/abs/math/0205068
dc.identifierJournal of Differential equations, 197 (2004), 197-217
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63999
dc.subjectAlgebraic Geometry
dc.subjectComplex Variables
dc.subject32L30; 14D05
dc.titleCenter conditions: Rigidity of logarithmic differential equations
dc.typetext

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