Orbits supporting bars within bars

High-resolution observations of the inner regions of barred disc galaxies h ave revealed many asymmetrical, small-scale central features, some of which are best described as secondary bars. Because orbital time-scales in the g alaxy centre are short, secondary bars are likely to be dynamically decoupl ed from the main kiloparsec-scale bars. Here we show that regular orbits ex ist in such doubly barred potentials, and that they can support the bars in their motion. We find orbits in which particles remain on loops: closed cu rves which return to their original positions after two bars have come back to the same relative orientation. Stars trapped around stable loops could form the building blocks for a long-lived, doubly barred galaxy. Using the loop representation, we can find which orbits support the bars in their mot ion, and the constraints on the sizes and shapes of self-consistent double bars. In particular, it appears that a long-lived secondary bar may exist o nly when an inner Lindblad resonance is present in the primary bar, and tha t it would not extend beyond this resonance.