Smooth linearization of germs of R 2 -actions and holomorphic vector fields
Dumortier, F. ; Roussarie, Robert
Annales de l'Institut Fourier, Tome 30 (1980), p. 31-64 / Harvested from Numdam
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Cet article contient une condition générique permettant la linéarisation en classe 𝒞 k , 0≤k≤∞, des germes d’actions infinitésimales singulières de R 2 sur R n (n≥2) et de champs de vecteurs holomorphes singuliers sur C n (n≥1). Cela généralise un résultat de S. Sternberg pour les germes de champs de vecteurs réels, singuliers, sur R n .

The paper contains a generic condition permitting the linearization in class 𝒞 k , 0≤k≤∞, of germs of singular infinitesimal R 2 -actions on R n (n≥2) and of singular holomorphic vector fields on C n (n≥1). It generalizes a similar result of S. Sternberg for germs of singular (real) vector fields on R n .

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     author = {Dumortier, F. and Roussarie, Robert},
     title = {Smooth linearization of germs of $R^2$-actions and holomorphic vector fields},
     journal = {Annales de l'Institut Fourier},
     volume = {30},
     year = {1980},
     pages = {31-64},
     doi = {10.5802/aif.774},
     mrnumber = {81k:58060},
     zbl = {0418.58015},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1980__30_1_31_0}
}

Dumortier, F.; Roussarie, Robert. Smooth linearization of germs of $R^2$-actions and holomorphic vector fields. Annales de l'Institut Fourier, Tome 30 (1980) pp. 31-64. doi : 10.5802/aif.774. http://gdmltest.u-ga.fr/item/AIF_1980__30_1_31_0/

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