# Doubling the variables in equations and sets of ordinary differential equations

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Abstract:

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.