On Lie's symmetries for planar polynomial differential systems (Q2730687)

A function \(V(x,y)\) is called an inverse integrating factor for the planar system NEWLINE\[NEWLINE\dot x=P(x,y), \quad\dot y=Q(x,y),NEWLINE\]NEWLINE if NEWLINE\[NEWLINEP{\partial V \over \partial x}+Q{\partial V\over\partial y}=(P_x+Q_y) \cdot VNEWLINE\]NEWLINE holds. The authors investigate polynomial planar systems and give results concerning connections between the existence of polynomial inverse integrating factors, polynomial first integrals and polynomial symmetry generators.NEWLINENEWLINENEWLINEThe results are then extended to the case of rational first integrals and symmetry generators. Some examples are given.