Dynamics of generic 1-parameter perturbations of a vector field with a singular point of codimension k

Arnaud Chéritat, Chrisitane Rousseau

The paper describes the bifurcation diagram of germs of generic $1$-parameter families of complex vector fields $\dot{z}={\omega }_{\epsilon }(z)$ on $\mathbb{C}$, unfolding a singular point of mul…