A three dimensional investigation of two dimensional orbits
  Orbits in the principal planes of triaxial potentials are known to be prone
to unstable motion normal to those planes, so that three dimensional
investigations of those orbits are needed even though they are two dimensional.
We present here an investigation of such orbits in the well known logarithmic
potential which shows that the third dimension must be taken into account when
studying them and that the instability worsens for lower values of the forces
normal to the plane. Partially chaotic orbits are present around resonances,
but also in other regions. The action normal to the plane seems to be related
to the isolating integral that distinguishes regular form partially chaotic
orbits, but not to the integral that distinguishes partially from fully chaotic
orbits.
