The role of resonances in barred galaxies
  The dynamics of the inner disk of many galaxies is dominated by bars. As a result, resonances between the bar and the disk become an important factor. In order to detect resonances, we measure angular and radial frequencies of individual orbits in N-body models of barred galaxies. In our simulations with several million particles, stellar disks are immersed in live halos of dark matter. A bar forms spontaneously and interacts with the disk through resonances. We detect 9 of them. The corotation (CR) and the inner Lindblad resonance (ILR) are the most significant. The spatial distributions of particles trapped at these resonances show that ILR is not localized at a given radius. Particles trapped at ILR lie along the bar spanning a wide range of radii. On the other hand, particles at the corotation resonance form a ring around the corotation radius. We study how orbits evolve near corotation and how they are trapped. When an orbit is getting trapped, it evolves strongly, but after that there is little evolution. Those trapped orbits circulate along the corotation ring or librate around a stable lagragian point. The same technique is applied to study resonances in the halo. The bar interacts strongly with the halo particles that stay close to the disk. We find the corotation resonance and the inner Lindblad resonance for halo particles. 
Daniel Ceverino and Anatoly Klypin (NMSU)