In this thesis, we explain finite cyclicity of a - family of vector fields with nilpotent singularity of saddle type of codimension 3 and define a new normal form for unfolding of this family. To describe the different types of graphics, we use a weighted blow-up for the singular point. Then, we explain two different types of Dulac maps in the blown-up family and develop a general method to prove that some regular transition maps have a nonzero higher derivative at a point.