Transition between order and chaos in a composite disk galaxy model with
  a massive nucleus and a dark matter halo
  We investigate the transition from regular to chaotic motion in a composite
galaxy model with a disk-halo, a massive dense nucleus and a dark halo
component. We obtain relationships connecting the critical value of the mass of
the nucleus or the critical value of the angular momentum, with the mass of the
dark halo, where the transition from regular motion to chaos occurs. We also
present 3D diagrams connecting the mass of nucleus the energy and the
percentage of stars that can show chaotic motion. The fraction of the chaotic
orbits observed in the phase plane, as a function of the mass of the dark halo
is also computed. We use a semi-numerical method, that is a combination of
theoretical and numerical procedure. The theoretical results obtained using the
version 8.0 of the Mathematica package, while all the numerical calculations
were made using a Bulirsch-Stoer FORTRAN routine in double precision. The
results can be obtained in semi-numerical or numerical form and give good
description for the connection of the physical quantities entering the model
and the transition between regular and chaotic motion. We observe that the mass
of the dark halo, the mass of the dense nucleus and the L_z component of the
angular momentum, are important physical quantities, as they are linked to the
regular or chaotic character of orbits in disk galaxies described by the model.
Our numerical experiments suggest, that the amount of the dark matter plays an
important role in disk galaxies represented by the model, as the mass of the
halo affects, not only the regular or chaotic nature of motion but it is also
connected with the existence of the different families of regular orbits.
Comparison of the present results with earlier work is also presented.
