Orbit evolution in growing stellar bars: Bar-supporting orbits at the
  vertical ILR region
  We investigate the evolution of orbital shapes at the Inner Lindblad
Resonance region of a rotating three-dimensional bar, the mass of which is
growing with time. We evaluate in time-dependent models, during a 5 Gyr period,
the importance of orbits with initial conditions known to play a significant
role in supporting peanut-like structures in autonomous systems. These orbits
are the central family of periodic orbits (x1) and vertical perturbations of
it, orbits of its standard three-dimensional bifurcations at the region (x1v1
and x1v2), as well as orbits in their neighbourhood. The knowledge of the
regular or chaotic character of these orbits is essential as well, because it
allows us to estimate their contribution to the support of a rotating bar and,
more importantly, the dynamical mechanisms that make it possible. This is
calculated by means of the GALI2 index. We find that orbital patterns existing
in the autonomous case, persist for longer times in the more massive bar
models, and even more so in a model in which the central spheroid component of
our adopted galactic potential becomes rather insignificant. The
peanut-supporting orbits which we find, have a regular or, in most cases, a
weakly chaotic character. There are cases in which orbits starting close to
unstable periodic orbits in an autonomous model behave as regular and support
the bar when its mass increases with time. An approximation for the orbital
dynamics of our non-autonomous models at a certain time, can be considered that
of the corresponding frozen system around that time.
