Normal forms for certain singularities of vectorfields
Takens, Floris
Annales de l'Institut Fourier, Tome 23 (1973), p. 163-195 / Harvested from Numdam
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On donne des formes normales C ∞ pour les singularités des champs C ∞ sur R qui ne sont pas plats et pour les champs C ∞ ,X sur R 2 , tels que X(0)=0 ; le jet d’ordre un de X (dans l’origine) est une rotation pure et un jet d’ordre supérieur de X contient une contraction ou une expansion.

C ∞ normal forms are given for singularities of C ∞ vectorfields on R, which are not flat, and for C ∞ vectorfields X on R 2 with X(0)=0, the 1-jet of X in the origin is a pure rotation, and some higher order jet of X attracting or expanding.

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     author = {Takens, Floris},
     title = {Normal forms for certain singularities of vectorfields},
     journal = {Annales de l'Institut Fourier},
     volume = {23},
     year = {1973},
     pages = {163-195},
     doi = {10.5802/aif.467},
     mrnumber = {51 \#1872},
     zbl = {0266.34046},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1973__23_2_163_0}
}

Takens, Floris. Normal forms for certain singularities of vectorfields. Annales de l'Institut Fourier, Tome 23 (1973) pp. 163-195. doi : 10.5802/aif.467. http://gdmltest.u-ga.fr/item/AIF_1973__23_2_163_0/

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