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

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