Characterization of a monodromic singular point of a planar vector field

The Newton diagram and the lowest-degree quasi-homogeneous terms of an analytic planar vector field allow us to determine whether an isolated singular point of the vector field is monodromic or has a characteristic trajectory.

► We rank the orbits that tend to a singular point of a planar differential system providing a relationship among them. ► We describe the characteristic orbits from the edges and vertices of its Newton diagram. ► We analyze the topological equivalence near a singular point and the monodromy problem.