Further reduction of normal forms for vector fields (Q5948206)

The author considers a vector field on the plane with a singularity at the origin. The singularity is assumed to be either of Hopf type (the linear part of the vector field has two purely imaginary eigenvalues) or of Bogdanov-Takens type (the linear part is nilpotent). The Lie method is used to reduce the number of coefficients in the nonlinear part of the normal form.