Ordinary Differential Equations
On the C1 normal forms for hyperbolic vector fields
Comptes Rendus. Mathématique, Volume 336 (2003) no. 9, pp. 709-712.

Given two germs of hyperbolic vector fields associated to autonomous ordinary differential equations x ˙= Ax + and y ˙= By +, where x,yR 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.

Etant donnés deux germes de champs de vecteurs hyperboliques définis par des équations différentielles autonomes x ˙= Ax + et y ˙= By +, où x,yR 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.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-073X(03)00173-0
Ren, Zhihua 1; Yang, Jiazhong 1

1 LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, PR China
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Ren, Zhihua; Yang, Jiazhong. 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. http://www.numdam.org/articles/10.1016/S1631-073X(03)00173-0/

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The work is supported by NSFC-10271006.