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Center conditions: rigidity of logarithmic differential equations
- Source :
-
Journal of Differential Equations . Feb2004, Vol. 197 Issue 1, p197. 21p. - Publication Year :
- 2004
-
Abstract
- In this paper, we prove that any degree <f>d</f> 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 <f>(&ast;)</f> 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. [Copyright &y& Elsevier]
- Subjects :
- *POLYNOMIALS
*DIFFERENTIAL equations
*HAMILTONIAN systems
*MATHEMATICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 197
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 11886380
- Full Text :
- https://doi.org/10.1016/j.jde.2003.07.002