  This paper aims to illustrate the applications of resonant Hamiltonian normal
forms to some problems of galactic dynamics. We detail the construction of the
1:1 resonant normal form corresponding to a wide class of potentials with
self-similar elliptical equi-potentials and apply it to investigate relevant
features of the orbit structure of the system. We show how to compute the
bifurcation of the main periodic orbits in the symmetry planes of a triaxial
ellipsoid and in the meridional plane of an axi-symmetric spheroid and briefly
discuss how to refine these results with higher-order approaches.
