Order and chaos in galactic maps

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We investigate the properties of motion in a map model derived from a galactic Hamiltonian made up of perturbed elliptic oscillators. The phase space portrait is obtained in all three different cases using the map and numerical integration of the equations of motion. Our numerical calculations suggest that the map describes very well the properties of regular motion in all three cases. There are cases where the map fails to describe chaotic motion and cases where the map describes satisfactorily the chaotic phase plane. We also compare the Lyapunov characteristic number and the spectra of orbits derived by the map and numerical integration in each case. The agreement of the outcomes is satisfactory.