On the planar integrable differential systems

Abstract

In this paper, we prove that the C 1 planar differential systems that are integrable and non-Hamiltonian roughly speaking are C 1 equivalent to the linear differential systems $${\dot u= u}$$ , $${\dot v= v}$$ . Additionally, we show that these systems have always a Lie symmetry. These results are improved for the class of polynomial differential systems defined in $${\mathbb{R}^2}$$ or $${\mathbb{C}^2}$$ .