  We investigate the dynamics in the logarithmic galactic potential with an
analytical approach. The phase-space structure of the real system is
approximated with resonant detuned normal forms constructed with the method
based on the Lie transform. Attention is focused on the properties of the axial
periodic orbits and of low order `boxlets' that play an important role in
galactic models. Using energy and ellipticity as parameters, we find analytical
expressions of several useful indicators, such as stability-instability
thresholds, bifurcations and phase-space fractions of some orbit families and
compare them with numerical results available in the literature.
