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

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.

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.

@article{AIF_1973__23_2_163_0,
     author = {Takens, Floris},
     title = {Normal forms for certain singularities of vectorfields},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {23},
     number = {2},
     year = {1973},
     pages = {163-195},
     doi = {10.5802/aif.467},
     zbl = {0266.34046},
     mrnumber = {51 \#1872},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1973__23_2_163_0}
}
Takens, Floris. Normal forms for certain singularities of vectorfields. Annales de l'Institut Fourier, Volume 23 (1973) no. 2, pp. 163-195. doi : 10.5802/aif.467. http://www.numdam.org/item/AIF_1973__23_2_163_0/

[1] J. Dieudonné, Foundations of Modern Analysis, Acad. Press, New York, 1960. | MR 22 #11074 | Zbl 0100.04201

[2] S. Kobayashi and K. Nomizu, Foundations of differential geometry vol. 1, Interscience, New York, 1963. | MR 27 #2945 | Zbl 0119.37502

[3] R. Narasimhan, Analysis on real and complex manifolds, North-Holland, Amsterdam, 1968. | MR 40 #4972 | Zbl 0188.25803

[4] S. Sternberg, Local contractions and a theorem of Poincaré, Amer. J. Math. vol. LXXIX (1957), 809-824. | MR 20 #3335 | Zbl 0080.29902

[5] F. Takens, Singularities of vectorfields, to appear in Publ. I. H. E. S.. | Numdam | Zbl 0279.58009

[6] F. Takens, Derivations of vectorfields, to appear in Comp. Math.. | Numdam | Zbl 0258.58005