ODE Admitting Two-dimensional Algebras of Dynamic Symmetries - Timoshin, M.I. (Journal of Applied Nonlinear Dynamics, 2026)
A generalization of S. Lie’s classification of second order ODEs on two-dimensional algebras of point symmetries is constructed. First integrals for found types second order ODEs are reduced. The pos- sibility of the determination of two-dimensional algebras of dynamic symmetries over number field is considered. Interconnection of dy- namic and contact symmetries is demonstrated. On a concrete ex- ample it is shown the procedure of the decomposition of a contact transformation into superposition of point transformation and Leg- endre transformation.