  We investigate the dynamics in a galactic potential with two reflection
symmetries. The phase-space structure of the real system is approximated with a
resonant detuned normal form constructed with the method based on the Lie
transform. Attention is focused on the stability properties of the axial
periodic orbits that play an important role in galactic models. Using energy
and ellipticity as parameters, we find analytical expressions of bifurcations
and compare them with numerical results available in the literature.
