On the local structure of real vector fields at a dicritical singularity (Q1286353)

The author considers \(C^\infty\) vector fields \(X\) defined near a singular point which we take as being \(0\in \mathbb{R}^n\). Let \(k\geq 1\) be the degree of the first nonzero jet of \(X\) at \(0\in \mathbb{R}^n\). The author also supposes that \(0\in \mathbb{R}^n\) is an algebraically isolated singularity of \(X\). She proves a topological finite determinacy theorem for a generic family of germs of \(C^\infty\) vector fields at a dicritical singularity in dimension three.