  The phase-space structure of two families of galactic potentials is
approximated with a resonant detuned normal form. The normal form series is
obtained by a Lie transform of the series expansion around the minimum of the
original Hamiltonian. Attention is focused on the quantitative predictive
ability of the normal form. We find analytical expressions for bifurcations of
periodic orbits and compare them with other analytical approaches and with
numerical results. The predictions are quite reliable even outside the
convergence radius of the perturbation and we analyze this result using
resummation techniques of asymptotic series.
