Topological Equivalence of Planar Vector Fields and Their Generalised Principal Part

Let (R2) be the space of C∞ planar vector fields. We consider the space V (R2) of vector fields with an isolated singularity and a fixed Newton diagram. We define the generalised principal part XΔ of the vector field X V and give the nondegeneracy condition on XΔ, using the Newton diagram. We prove that X V is locally topologically equivalent to its minimal generalised principal part XΔ, if XΔ is nondegenerate and X is not a monodromic vector field. In the proof we use the normal form method and the blowing-up method.