On sufficient conditions for integrability of a planar system of ODEs near a degenerate stationary point

Abstract

We consider an autonomous system of ordinary differential equations, which is solved with respect to derivatives. To study the local integrability of the system near a degenerate stationary point we use an approach based on the Power Geometry Method and on the computation of resonant normal forms. For a planar system depending on five parameters we give four series of conditions on parameters of the system for which it is integrable near the degenerate stationary point. © 2010 Springer-Verlag Berlin Heidelberg.