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- W1963535464 abstract "Soit X=(x∂∂y−y∂∂x)+f(x,y)∂∂x+g(x,y)∂∂y un champ de vecteurs polynomial de degré n du plan R2. En utilisant la théorie des formes prénormales de J. Ecalle, on caractérise les perturbations donnant naissance à un centre. On décrit ensuite la structure des monômes résonnants, en utilisant une caractérisation géométrique (l'invariance sous une action de C∗) de ces monômes. On obtient un théorème de décomposition qui permet d'écrire chacun de ces monômes comme produit de monômes universels. On résout alors le problème de lecture dans le cas des conditions algébriques du centre réversible, pour une perturbation polynomiale de degré quelconque. Let X=(x∂∂y−y∂∂x)+f(x,y)∂∂x+g(x,y)∂∂y be a polynomial vector field of degree n in R2. Using the prenormal form theory of J. Ecalle, we characterize perturbations which give rise to a center. We describe the structure of the resonants monomials using a geometric characterization (invariance under a C∗-action) of these monomials. We obtain a decomposition theorem which allow us to write these monomials as product of universal monomials. We then solve, for any degree, the reading problem for the reversible center algebraic conditions." @default.
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- W1963535464 date "2001-04-01" @default.
- W1963535464 modified "2023-09-25" @default.
- W1963535464 title "Formes normales et problème du centre" @default.
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- W1963535464 doi "https://doi.org/10.1016/s0007-4497(00)01070-8" @default.
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