Divergence and Poincaré-Liapunov constants for analytic differential systems

•We give a formula for the first Poincaré-Liapunov constant using the divergence, when the nonlinear terms start with odd degree.•Both nondegenerate and nilpotent monodromic singular points are considered.•We prove that a sign definite divergence gives the stability of the singular point.

We consider a planar autonomous real analytic differential system with a monodromic singular point p. We deal with the center problem for the singular point p. Our aim is to highlight some relations between the divergence of the system and the Poincaré-Liapunov constants of p when these are defined.