Nilpotent singularities in generic 4-parameter families of 3-dimensional vector fields (Q1914829)

The paper deals with singularities of vector fields in \(\mathbb{R}^3\) having a 1-jet linear conjugate to \(y\bigl(\frac{\partial}{\partial x}\bigr)+z\bigl(\frac{\partial}{\partial y}\bigr)\). The authors prove that in codimension 3 all singularities are mutually \(C^0\) equivalent. A very interesting result is that for codimension 4 there are exactly 5 types of singularities for \(C^0\) equivalence. The proof is based on normal form theory, blowing-up, and estimation of Abelian integrals.