Dynamical rules for barred spiral galaxies

Numerical integrations of 2D-orbits demonstrate that the principal family of periodic orbits in strong barred potentials is the prograde parallel family. All other families have orbit density distributions which are inconsistent with the imposed potential. Some important implications are discussed: (1) bars tumble in the sense of galactic rotation; (2) corotation must lie outside the bar distortion; (3) strong rapidly tumbling bars are cold, and, conversely, strong slowly tumbling bars are hot and (4) the magnitude of the bar distortion is limited to axial ratios of about 1:5, due to the onset of stochasticity well inside corotation. A small population of stars on stochastic orbits may form the more nearly axisymmetric lens structure seen in some barred galaxies.