Lie transforms and the Hamiltonization of non-Hamiltonian systems

To develop the perturbation solution of the non-Hamiltonian system of differential equationsy=g(y, t; ), it is sufficient to obtain the perturbation solution of a Hamiltonian system represented by the HamiltonianK=Y·g(y, t; ) which is linear in the adjoint vectorY. This Hamiltonization allows the direct use of the perturbation methods already established for Hamiltonian systems. To demonstrate this fact, a Hamiltonian algorithm developed by this author and based on the Lie-Deprit transform is applied to the Hamiltonized system and is shown to be equivalent to the application of the non-Hamiltonian form of this same algorithm to the original non-Hamiltonian system.