  We use a composite gravitational galactic model consisting of a disk, a halo,
a massive nucleus and a strong nuclear bar, in order to study the connections
between global and local parameters in a realistic dynamical system. The local
model is constructed from a two-dimensional perturbed harmonic oscillator and
can be derived by expanding the global model in the vicinity of the central
stable Lagrange equilibrium point. The frequencies of oscillations are not
arbitrary, but they are connected with all the parameters involved with the
global model. Moreover, the value of the local energy is also connected with
the value of the global energy. Low and high energy stars in the global model
display chaotic motion. Comparison with previous research reveals that the
presence of the massive nucleus is responsible for the chaotic motion of the
low energy stars. In the local motion, the low energy stars show interesting
resonance phenomena, but the chaotic motion, if any, is negligible. On the
contrary, the high energy stars do not show bounded motion in the local model.
This is an indication of particular activity near the center of galaxies
possessing massive nuclei.
