LIE TRANSFORMS FOR ORDINARY DIFFERENTIAL EQUATIONS: TAKING ADVANTAGE OF THE HAMILTONIAN FORM OF TERMS OF THE PERTURBATION

In the context of Lie transforms theory applied to ordinary di erential systems, we deal with the case for which part of the perturbing equation admits a Hamiltonian formulation. This fact allows to perform a Lie transform combining a treatment of vector type with another of Hamiltonian character. We show that this produces a reduction in the number of operations involved in the algorithms. We illustrate the algorithms with an example.