  Analytic methods to investigate periodic orbits in galactic potentials. To
evaluate the quality of the approximation of periodic orbits in the logarithmic
potential constructed using perturbation theory based on Hamiltonian normal
forms. The solutions of the equations of motion corresponding to periodic
orbits are obtained as series expansions computed by inverting the normalizing
canonical transformation. To improve the convergence of the series a
resummation based on a continued fraction may be performed. This method is
analogous to that looking for approximate rational solutions (Prendergast
method). It is shown that with a normal form truncated at the lowest order
incorporating the relevant resonance it is possible to construct quite accurate
solutions both for normal modes and periodic orbits in general position.
