Smooth linearization of germs of $R^2$-actions and holomorphic vector fields

Dumortier, F.; Roussarie, Robert

Annales de l'Institut Fourier, Tome 30 (1980) no. 1, pp. 31-64.

Cet article contient une condition générique permettant la linéarisation en classe ${𝒞}^k$, $0\le k\le \infty$, des germes d’actions infinitésimales singulières de ${\mathbf{R}}^2$ sur ${\mathbf{R}}^n$ $(n\ge 2)$ et de champs de vecteurs holomorphes singuliers sur ${\mathbf{C}}^n$ $(n\ge 1)$. Cela généralise un résultat de S. Sternberg pour les germes de champs de vecteurs réels, singuliers, sur ${\mathbf{R}}^n$.

The paper contains a generic condition permitting the linearization in class ${𝒞}^k$, $0\le k\le \infty$, of germs of singular infinitesimal ${\mathbf{R}}^2$-actions on ${\mathbf{R}}^n$ $(n\ge 2)$ and of singular holomorphic vector fields on ${\mathbf{C}}^n$ $(n\ge 1)$. It generalizes a similar result of S. Sternberg for germs of singular (real) vector fields on ${\mathbf{R}}^n$.

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