  A 3D dynamical model is used to study the motion in the central parts of an
elliptical galaxy, hosting a massive and dense nucleus. Our aim is to
investigate the regular or chaotic character of the motion, with emphasis in
the different chaotic components, as well as the sticky regions of the
dynamical system. In order to define the character of the motion in the 2D
system, we use the classical method of the Poincare x-px phase plane, the
Lyapunov Characteristic Exponent (LCE) and the dynamical parameter - the S(c)
spectrum. Then the results obtained from the 2D system are used to investigate
the properties of the 3D system. For this, we introduce and use a new dynamical
parameter, the S(k) spectrum, which proves to be a very reliable and fast
method to detect the islandic motion and the evolution of the sticky orbits in
the 3D system. Numerical experiments conducted by the new S(k) spectrum suggest
that the different chaotic components in the 3D system do not interact for time
intervals much larger than the age of the galaxy. The results indicate that the
different sticky regions do not lead to a unified chaotic sea. Thus, the
behavior of the 3D sticky orbits differs from that observed in the 2D system.
Furthermore, the 3D motion near the center of a triaxial elliptical galaxy
seems to be very complicated, displaying several families of resonant orbits,
different chaotic components and sticky regions, while only a small fraction of
orbits is regular. The comparison with earlier results reveals the importance
of the conception of the new dynamical spectrum.
