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Forme normale formelle d'une perturbation à séparatrices fixées d'un champ hamiltonien quasi-homogène

Emmanuel Paul
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Abstract

On classifie à changement de variable formel près les champs de vecteurs --ainsi que les feuilletages qu'ils définissent-- qui sont des perturbations d'un champ hamiltonien quasi-homogène $X_0$ par des termes de degré de quasi-homogénéité sup'erieur. Le degré $δ_0$ du champ $X_0$ est quelconque, mais on demande que le champ perturbé laisse encore invariant les séparatrices de $X_0$. Les formes normales présentées ici généralisent celles obtenues lorsque $X_0$ possède une partie linéaire semi-simple ou nilpotente. Nous les interpr'etons g'eom'etriquement en terme de cohomologie relative au champ initial.

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BibTeXRIS

Emmanuel Paul. 2003-03-18. Forme normale formelle d'une perturbation à séparatrices fixées d'un champ hamiltonien quasi-homogène. https://arxiv.org/abs/math/0303216

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