Global dynamics of triaxial galactic models through frequency map analysis

In a previous article (Papaphilippou&Laskar 1996), we used the frequency map analysis for studying the dynamics of the axisymmetric softened version of the logarithmic potential. The method is now applied to its 3-dimensional generalisation in order to deepen our knowledge regarding the dynamics of triaxial power-law galactic models. The principal dynamical features of the system are reviewed within the appropriate Hamiltonian frame of reference. The quasi-periodic approximations furnished by the method permit to clarify the dynamics of the principal types of orbits and their connection with perturbations of integrable cases of the general Hamiltonian. All the fine details of the dynamics associated with the addition of the third degree of freedom are displayed in the complete frequency map, a direct representation of the system’s Arnol’d web. The influence of resonant lines and the extent of the chaotic zones are directly visualized in the physical space of the system. This approach reveals many unknown dynamical features of triaxial galactic potentials and gives strong indications that chaos should be an innate characteristic of triaxial configurations. The impact of these results in the construction of self-consistent galactic models are finally discussed.