  In the present article, we present a new gravitational galactic model,
describing motion in elliptical as well as in disk galaxies, by suitably
choosing the dynamical parameters. Moreover, a new dynamical parameter, the
S(g) spectrum, is introduced and used, in order to detect islandic motion of
resonant orbits and the evolution of the sticky regions. We investigate the
regular or chaotic character of motion, with emphasis in the different
dynamical models and make an extensive study of the sticky regions of the
system. We use the classical method of the Poincare (r-pr) phase plane and the
new dynamical parameter of the S(g) spectrum. The LCE is used, in order to make
an estimation of the degree of chaos in our galactic model. In both cases, the
numerical calculations, suggest that our new model, displays a wide variety of
families of regular orbits, compared to other galactic models. In addition to
the regular motion, this new model displays also chaotic regions. Furthermore,
the extent of the chaotic regions increases, as the value of the flatness
parameter b of the model increases. Moreover, our simulations indicate, that
the degree of chaos in elliptical galaxies, is much smaller than that in dense
disk galaxies. In both cases numerical calculations show, that the degree of
chaos increases linearly, as the flatness parameter b increases. In addition, a
linear relationship between the critical value of angular momentum and the b
parameter if found, in both cases (elliptical and disk galaxies). Some
theoretical arguments to support the numerical outcomes are presented.
Comparison with earlier work is also made.
