Dynamical symmetries of autonomous differential second order equations

Abstract:
The principal instrument, which has been invented and used by  S.Lie is exposition of properties of the differential equations with the help of groups. In the offered report the possibility of use of dynamic symmetries to an analytical integration of autonomous ODE of the second order is presented. The correlation with known results is marked. The concept of a defining system of dynamic symmetries is given. The example indicating to the effectiveness of an offered method is producced.