A relationship between lambda-symmetries and first integrals for ordinary differential equations

摘要

In this paper, we provide some geometric properties of lambda -symmetries of ordinary differential equations using vector fields and differential forms. According to the corresponding geometric representation of lambda -symmetries, we conclude that first integrals can also be derived if the equations do not possess enough symmetries. We also investigate the properties of lambda -symmetries in the sense of the deformed Lie derivative and differential operator. We show that lambda -symmetries have the exact analogous properties as standard symmetries if we take into consideration the deformed cases.