Interplay Between Chaotic and Regular Motion in a Time-Dependent Barred
  Galaxy Model
  We study the distinction and quantification of chaotic and regular motion in
a time-dependent Hamiltonian barred galaxy model. Recently, a strong
correlation was found between the strength of the bar and the presence of
chaotic motion in this system, as models with relatively strong bars were shown
to exhibit stronger chaotic behavior compared to those having a weaker bar
component. Here, we attempt to further explore this connection by studying the
interplay between chaotic and regular behavior of star orbits when the
parameters of the model evolve in time. This happens for example when one
introduces linear time dependence in the mass parameters of the model to mimic,
in some general sense, the effect of self-consistent interactions of the actual
N-body problem. We thus observe, in this simple time-dependent model also, that
the increase of the bar's mass leads to an increase of the system's chaoticity.
We propose a new way of using the Generalized Alignment Index (GALI) method as
a reliable criterion to estimate the relative fraction of chaotic vs. regular
orbits in such time-dependent potentials, which proves to be much more
efficient than the computation of Lyapunov exponents. In particular, GALI is
able to capture subtle changes in the nature of an orbit (or ensemble of
orbits) even for relatively small time intervals, which makes it ideal for
detecting dynamical transitions in time-dependent systems.
