On the stability criteria for equatorial circular orbits in Galactic
  Dynamics: I.Newtonian Thin Disks
  We make a revision of the stability criteria for equatorial circular orbits,
obtained from the epicyclic approximation, which is widely used in Newtonian
models for axisymmetric galaxies. We find that, for the case of thin disk
models, the criteria of vertical stability must be reformulated, due to the
discontinuity in the gravitational field. We show that, for a model
characterized by a surface mass density $\Sigma$, the necessary and sufficient
condition to have vertically stable orbits is that $\Sigma>0$. On the other
hand, the criteria for radial stability is the same as in thick diks, i.e. that
the epicyclic frequency is positive.
