Singularities of Cubic Vector Fields on the Plane

Abstract

The main aim of this paper is to prove that a families of some cubicvector fields on 2 – dimensional manifolds ,all singularities withcharacteristic orbits are topologically determined by a finite set,moreover we prove that two singularities (R 2 ,0 v ,X) and (R 2 ,0 v ,X )are Cο - equivalent after polar blowing up ,provided there ischaracteristic orbits.