2016MNRAS.463.3965J

A three degrees of freedom (3-dof) barred galaxy model composed of a spherically symmetric nucleus, a bar, a flat disc and a spherically symmetric dark matter halo is used for investigating the dynamics of the system. We use colour-coded plots to demonstrate how the value of the semimajor axis of the bar influences the regular or chaotic dynamics of the 3-dof system. For distinguishing between ordered and chaotic motion, we use the Smaller ALingment Index (SALI) method, a fast yet very accurate tool. Undoubtedly, the most important elements of the dynamics are the normally hyperbolic invariant manifolds (NHIMs) located in the vicinity of the index 1 Lagrange points L2 and L3. These manifolds direct the flow of stars over the saddle points, while they also trigger the formation of rings and spirals. The dynamics in the neighbourhood of the saddle points is visualized by bifurcation diagrams of the Lyapunov orbits as well as by the restriction of the Poincare map to the NHIMs. In addition, we reveal how the semimajor axis of the bar influences the structure of these manifolds which determine the final stellar structure (rings or spirals). Our numerical simulations suggest that in galaxies with weak bars the formation of R1 rings or R_1^' pseudo-rings is favoured. In the case of galaxies with intermediate and strong bars, the invariant manifolds seem to give rise to R1R2 rings and twin spiral formations, respectively. We also compare our numerical outcomes with earlier related work and with observational data.