no. 2
Normal forms for certain singularities of vectorfields
Annales de l'Institut Fourier, Tome 23 (1973) no. 2, pp. 163-195.

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},
     pages = {163--195},
     publisher = {Institut Fourier},
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     volume = {23},
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     year = {1973},
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Takens, Floris. Normal forms for certain singularities of vectorfields. Annales de l'Institut Fourier, Tome 23 (1973) no. 2, pp. 163-195. doi : 10.5802/aif.467. https://aif.centre-mersenne.org/articles/10.5802/aif.467/

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