Chaoticity in the vicinity of complex unstable periodic orbits in
  galactic type potentials
  We investigate the evolution of phase space close to complex unstable
periodic orbits in two galactic type potentials. They represent characteristic
morphological types of disc galaxies, namely barred and normal (non-barred)
spiral galaxies. These potentials are known for providing building blocks to
support observed features such as the peanut, or X-shaped bulge, in the former
case and the spiral arms in the latter. We investigate the possibility that
these structures are reinforced, apart by regular orbits, also by orbits in the
vicinity of complex unstable periodic orbits. We examine the evolution of the
phase space structure in the immediate neighbourhood of the periodic orbits in
cases where the stability of a family presents a successive transition from
stability to complex instability and then to stability again, as energy
increases. We find that we have a gradual reshaping of invariant structures
close to the transition points and we trace this evolution in both models. We
conclude that for time scales significant for the dynamics of galaxies, there
are weakly chaotic orbits associated with complex unstable periodic orbits,
which should be considered as structure-supporting, since they reinforce the
morphological features we study.
