The Geometrical Demonstration of the Order of Resonant Saddle Points in $${\mathbb {C}}^2$$C2

Here we investigate the Minkowski box dimension of complex integral curves of the vector fields near resonant saddles in $${\mathbb {C}}^2$$. The results provide the geometrical explanation of the order of the saddle points and a quantitative description for the non-integrability via monodromy.