Resonances and bifurcations in systems with elliptical equipotentials
  We present a general analysis of the orbit structure of 2D potentials with
self-similar elliptical equipotentials by applying the method of Lie transform
normalization. We study the most relevant resonances and related bifurcations.
We find that the 1:1 resonance is associated only to the appearance of the
loops and leads to the destabilization of either one or the other normal modes,
depending on the ellipticity of equipotentials. Inclined orbits are never
present and may appear only when the equipotentials are heavily deformed. The
1:2 resonance determines the appearance of bananas and anti-banana orbits: the
first family is stable and always appears at a lower energy than the second,
which is unstable. The bifurcation sequence also produces the variations in the
stability character of the major axis orbit and is modified only by very large
deformations of the equipotentials. Higher-order resonances appear at
intermediate or higher energies and can be described with good accuracy.
