Chaos in Orbits Due to Disk Crossings

We study orbits of halo stars in some simple models of galaxies with disks and halos, to see whether the cumulative eects of the sudden changes in acceleration which occur at disk crossings can induce chaos. We nd that they can, though not in all orbits and not in all potentials. Most of the orbits which become chaotic stay relatively close to the disk, and range widely in the radial direction. Heavier disks and increased halo attening both enhance the extent of the chaos. A limited range of experiments with a three{component model of the Milky Way with an added central bulge nds that many chaotic disk{crossing orbits can be expected in the central regions, and that prolateness of the halo is much more eective than oblateness in generating chaos