  We show how to use extended word series in the reduction of continuous and
discrete dynamical systems to normal form and in the computation of formal
invariants of motion in Hamiltonian systems. The manipulations required involve
complex numbers rather than vector fields or diffeomorphisms. More precisely we
construct a group G and a Lie algebra g in such a way that the elements of G
and g are families of complex numbers; the operations to be performed involve
the multiplication F in G and the bracket of g and result in universal
coefficients that are then applied to write the normal form or the invariants
of motion of the specific problem under consideration.
