Chavarriga, J.; García, I. A.; Giné, J. On Lie’s symmetries for planar polynomial differential systems. (English) Zbl 0987.34027 Nonlinearity 14, No. 4, 863-880 (2001). A function \(V(x,y)\) is called an inverse integrating factor for the planar system \[ \dot x=P(x,y), \quad\dot y=Q(x,y), \] if \[ P{\partial V \over \partial x}+Q{\partial V\over\partial y}=(P_x+Q_y) \cdot V \] 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.The results are then extended to the case of rational first integrals and symmetry generators. Some examples are given. Reviewer: G.Czichowski (Greifswald) Cited in 10 Documents MSC: 34C14 Symmetries, invariants of ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 22E05 Local Lie groups Keywords:Lie’s symmetries; planar polynomial differential systems; symmetry generator; first integral; integrating factor; polynomial planar systems PDFBibTeX XMLCite \textit{J. Chavarriga} et al., Nonlinearity 14, No. 4, 863--880 (2001; Zbl 0987.34027) Full Text: DOI