  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.
