Divergence and Poincare-Liapunov constants for analytic differential systems

Abstract

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.

The first author is partially supported by a MINECO/FEDER grant number MTM2011-22877 and by an AGAUR (Generalitat de Catalunya) grant number 2014SGR 1204. The second author is partially supported by a MINECO/FEDER grant MTM2008-03437 and MTM2013-40998-P, an AGAUR grant number 2014SGR-568, an ICREA Academia, the grants FP7-PEOPLE- 2012-IRSES 318999 and 316338, FEDER-UNAB-10-4E-378.