Abstract
We investigate the properties of motion in a potential made up of two perturbed harmonic oscillators in the resonance case 1:2. This potential can be considered to describe the motion in the central parts of a barred galaxy. In order to visualize the properties of orbits we use a map which produces the x– p x Poincaré phase plane in the non-rotating as well as in the rotating case. Comparing the results of the map, with those found by numerical integration of the equation of motion, we find that the map describes very well the characteristic of motion in the non-rotating case. Good results are also obtained, for small values of the perturbation parameter, when the bar rotates at small angular velocity. Finally, we study the onset of chaos and compare the outcomes of this research with previous work on barred galaxies.
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