Doubling the variables in equations and sets of ordinary differential equations

The procedure for doubling the variables makes possible to construct an initial flow projector in the extremities field. This procedure contains a simple way of studying the robustness of solution of the initial set, to wit – the Lyapunov function is coincident with the Hamiltonian and as a result the determination of the robustness of the zeroth solution is reduced to that of signs of E (x, y) quadrics and signs of scalar product of E x-gradient by the initial flow of the non-variational set.