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},
     address = {Grenoble},
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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. http://www.numdam.org/articles/10.5802/aif.467/

[1] J. Dieudonné, Foundations of Modern Analysis, Acad. Press, New York, 1960. | MR | Zbl

[2] S. Kobayashi and K. Nomizu, Foundations of differential geometry vol. 1, Interscience, New York, 1963. | MR | Zbl

[3] R. Narasimhan, Analysis on real and complex manifolds, North-Holland, Amsterdam, 1968. | MR | Zbl

[4] S. Sternberg, Local contractions and a theorem of Poincaré, Amer. J. Math. vol. LXXIX (1957), 809-824. | MR | Zbl

[5] F. Takens, Singularities of vectorfields, to appear in Publ. I. H. E. S.. | Numdam | Zbl

[6] F. Takens, Derivations of vectorfields, to appear in Comp. Math.. | Numdam | Zbl

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