Integrability of motion around galactic razor-thin disks
  We consider the three-dimensional bounded motion of a test particle around
razor-thin disk configurations, by focusing on the adiabatic invariance of the
vertical action associated with disk-crossing orbits. We find that it leads to
an approximate third integral of motion predicting envelopes of the form
$Z(R)\propto[\Sigma(R)]^{-1/3}$, where $R$ is the radial galactocentric
coordinate, $Z$ is the z-amplitude (vertical amplitude) of the orbit and
$\Sigma$ represents the surface mass density of the thin disk. This third
integral, which was previously formulated for the case of flattened 3D
configurations, is tested for a variety of trajectories in different thin-disk
models.
