Resumen de Symmetries and First Integrals of Differential Equations

Jing Zhang, Yong Li

• It is known that an n-dimensional system of ordinary differential equations with Lie symmetry which involves a divergence-free Liouville vector field possesses n-1 independent first integrals (i.e., it is algebraically integrable) (Ünal in Phys. Lett. A 260:352�359, [1999]). In the present paper, we show that if an n-dimensional system of ordinary differential equations admits a C ?-symmetry vector field which satisfies some special conditions, then it also possesses n-1 independent first integrals. Several examples are given to illustrate our result.