We study the well-known logarithmic galactic potential through the frequency map analysis method of Laskar 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 impact of this new approach in galactic dynamics is investigated by applying the method to the axisymmetric version of the logarithmic potential. The reliability of the method is demonstrated via perturbative techniques and numerical transformations in action-angle variables. Comparison with previous studies involving Fourier methods are also given. By means of frequency map analysis, we provide a global vision of the dynamics of the planar potential for various values of the perturbation parameter. The location and extent of the chaotic zones can be easily visualised. All the important resonances are detected with their actual strength, as well as the associated periodic orbits. The method is then applied to the complete threedimensional version of the logarithmic potential. 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 extent of the chaotic zones and the influence of resonant lines 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.
