Differentiable conjugacy of the Poincaré type vector fields on $\mathbf \{R\}^3$

Abstract

We prove that on R 3 , except for those germs of vector fields whose linear parts are conjugated to λx∂/∂x + λy∂/∂y + 2λz∂/∂z, any two Poincare type vector fields are at least C 3 conjugated to each other provided their linear approximations have the same eigenvalues and the nonlinear parts are generic.