Using new dynamical indicators to distinguish between order and chaos in a galactic potential producing exact periodic orbits and chaotic components

The theory of the inverse problem is used in order to find a two dimensional galactic potential generating a mono-parametric family of elliptic periodic orbits. The potential is made up of a two-dimensional harmonic oscillator with perturbing terms of third and fourth degree and can be considered to describe local motion in the central parts of a barred galaxy. Our numerical calculations indicate that the potential produces also other families of orbits and there are cases, where distinct chaotic components are also observed. The numerical experiments suggest that there are regular as well as chaotic orbits supporting the barred structure. We use a variety of dynamical indicators, in order to determine the character of motion. Of significant interest, is the S(g) dynamical spectrum, which is used in order to identify the islandic motion of resonant orbits and also proves to be a very useful and fast indicator, in order to distinguish between regular and chaotic motion. Comparison with other methods for detecting chaos is also discussed. The present results are compared with outcomes from earlier work.