Surfaces with central configuration and Dulac's problem for a three dimensional isolated Hopf singularity

Nuria Corral, María Martín Vega, Fernando Sanz Sánchez

Let $\xi$ be a real analytic vector field with an elementary isolated singularity at $0\in {\mathbb{R}}^3$ and eigenvalues $\pm bi,c$ with $b,c\in \mathbb{R}$ and $b\ne 0$. We prove t…