A rational galactic potential with accurate periodic orbits and
  quasi-integrals of motion
  The motion in a simple, time independent rational galactic potential is
studied. The potential is a generalization of a two dimensional harmonic
oscillator potential and can be considered to describe plane motion in the
central parts of a galaxy. There are cases, where the potential displays
accurate periodic orbits, together with large chaotic regions. The starting
position of these orbits can be found using analytical arguments. Using a
quasi-integral of motion, we study the stability of the central periodic orbit
and explain the degree of chaos in the inner regions of the galaxy. Our
outcomes are compared with results coming from polynomial potentials with
accurate periodic orbits and large chaotic regions.
