ul 2 00 4 Center conditions : Rigidity of logarithmic differential equations 1 Hossein

نویسنده

  • Hossein Movasati
چکیده

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. We will also generalize J.P. Francoise recursion formula and (*) condition for a polynomial which is a product of lines in a general position. Some applications on the cyclicity of cycles and the Bautin ideals will be given.

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تاریخ انتشار 2004