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Comptes Rendus Mathématique
Volume 336, n° 9
pages 709-712 (mai 2003)
Doi : 10.1016/S1631-073X(03)00173-0
Received : 19 Mars 2003 ;  accepted : 19 Mars 2003
On the   normal forms for hyperbolic vector fields

Zhihua  Ren,  Jiazhong  Yang
LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, PR China 

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Given two germs of hyperbolic vector fields associated to autonomous ordinary differential equations   and  , where  , and   and   are   matrices, we prove that under some algebraic conditions on the eigenvalues of the matrices and genericity condition on the nonlinear terms, they are at least   conjugate if and only if   and   are similar. To cite this article: Z. Ren, J. Yang, C. R. Acad. Sci. Paris, Ser. I 336 (2003).

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Etant donnés deux germes de champs de vecteurs hyperboliques définis par des équations différentielles autonomes   et  , où  ,   et   sont des matrices d'ordre  , on démontre que, sous certaines conditions algébriques sur les valeurs propres des matrices et des conditions de non dégénérescensce des terms nonlinéaires, ils sont au moins   conjuqués si et seulement si   et   sont semblables. Pour citer cet article : Z. Ren, J. Yang, C. R. Acad. Sci. Paris, Ser. I 336 (2003).




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