Origin of chaos and orbital behaviour in slowly rotating triaxial models.

It is now well accepted that rotating triaxial models may provide good representations of stellar systems like elliptical galaxies, cD galaxies, spiral bulges or bars. These systems are known to possibly have very different structural and dynamical parameters such as axis ratios, figure rotation or central density slope. In order to understand the shape of such systems it is necessary to know the structure and stability of orbits in triaxial models. The main stable periodic orbits form the backbone around which the global structure is built, whereas unstable orbits can contribute to trigger chaos and evolution in the system. The purpose of the present paper is to give the main results of a systematic study of the periodic orbits, the resonances and the onset of chaos in models with various axis ratios, figure rotation and central mass concentration.