Topological equivalence of a plane vector field with its principal part defined through Newton Polyhedra

AbstractWe introduce a blowing-up of singularities of vector fields associated with Newton Polyhedra in the space of the exponents, by means of which we prove a generalization of the Hartman-Grobman Theorem, namely: a plane vector field possessing characteristic orbits is locally topologically equivalent with its principal part, under suitable non-degeneracy hypotheses. Under stronger hypotheses, a similar equivalence result is proven between a plane vector field and a single quasihomogeneous component of its principal part. The case of second order equations is also studied