On the C1 normal forms for hyperbolic vector fields

Abstract

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 C 1 conjugate if and only if A and B are similar. To cite this article: Z. Ren, J. Yang, C. R. Acad. Sci. Paris, Ser. I 336 (2003).