Comptes Rendus
no. 9
Ordinary Differential Equations
On the C1 normal forms for hyperbolic vector fields
[Sur la classification C1 des champs de vecteurs hyperboliques]

Présenté par : Bernard Malgrange

Zhihua Ren1 ; Jiazhong Yang1
1 LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, PR China
Comptes Rendus. Mathématique, Volume 336 (2003) no. 9, pp. 709-712.

Etant donnés deux germes de champs de vecteurs hyperboliques définis par des équations différentielles autonomes x ˙= Ax +⋯ et y ˙= By +⋯, où x,y∈R n , A et B sont des matrices d'ordre n, 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 C1 conjuqués si et seulement si A et B sont semblables.

Given two germs of hyperbolic vector fields associated to autonomous ordinary differential equations x ˙= Ax +⋯ and y ˙= By +⋯, where x,y∈R n , and A and B are n×n 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 C1 conjugate if and only if A and B are similar.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00173-0
Zhihua Ren 1 ; Jiazhong Yang 1

1 LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, PR China 
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Zhihua Ren; Jiazhong Yang. On the C1 normal forms for hyperbolic vector fields. Comptes Rendus. Mathématique, Volume 336 (2003) no. 9, pp. 709-712. doi : 10.1016/S1631-073X(03)00173-0. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00173-0/

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☆ The work is supported by NSFC-10271006.

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