Asymptotic expansion of a monodromy map

In the paper we compute the asymptotic series of the monodromy transformation of a monodromic singular point of a vector field in the plane when its Newton diagram consists of a single non-degenerate edge. The method of a resolution of singularities via Newton diagram is applied. A hypothesis about the existence of an algorithm for calculating the coefficients of correspondence maps and monodromy transformation containing no operation limit is put forward. This conjecture has been proved in the case of a single non-degenerate edge of the Newton diagram, as well as for the first two coefficients in the asymptotic expansion of the correspondence map in the first quadrant of the plane (as well as the monodromy transformation) in the case where the Newton diagram of the vector field consists of two non-degenerate edges.