Classifying orbits of low and high energy stars in axisymmetric disk
  galaxies
  The ordered or chaotic character of orbits of stars moving in the meridional
$(R,z)$ plane of an analytic axisymmetric time-independent disk galaxy model
with an additional spherically symmetric central nucleus is investigated. Our
aim is to determine how the total energy influences the orbital structure of
the galaxy. For this purpose we monitor how the percentage of chaotic orbits as
well as the rates of orbits composing the main regular families evolve as a
function of the value of the energy. In order to distinguish with certainty
between chaotic and ordered motion we use the SALI method in extensive sets of
initial conditions of orbits. Moreover, a spectral method is applied for
identifying the various regular families and also for recognizing the secondary
resonances that bifurcate from them. Our numerical computations suggest that
for low energy levels the observed amount of chaos is high and the orbital
content is rather poor, while for high energy levels, corresponding to global
motion, regular motion dominates and many secondary higher resonances emerge.
We also compared our results with previous related work.
