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This paper aims to illustrate the applications of resonant Hamiltonian normalforms to some problems of galactic dynamics. We detail the construction of the1:1 resonant normal form corresponding to a wide class of potentials withself-similar elliptical equi-potentials and apply it to investigate relevantfeatures of the orbit structure of the system. We show how to compute thebifurcation of the main periodic orbits in the symmetry planes of a triaxialellipsoid and in the meridional plane of an axi-symmetric spheroid and brieflydiscuss how to refine these results with higher-order approaches.

Relevance of the 1:1 resonance in galactic dynamics