Manifold spirals, disc-halo interactions and the secular evolution in
  N-body models of barred galaxies
  The manifold theory of barred-spiral structure provides a dynamical mechanism
explaining how spiral arms beyond the ends of galactic bars can be supported by
chaotic flows extending beyond the bar's co-rotation zone. We discuss its
applicability to N-body simulations of secularly evolving barred galaxies. In
these simulations, we observe consecutive `incidents' of spiral activity,
leading to a time-varying disc morphology. Besides disc self-excitations, we
provide evidence of a newly noted excitation mechanism related to the
`off-centering' effect: particles ejected in elongated orbits at major
incidents cause the disc center-of-mass to recoil and be set in a wobble-type
orbit with respect to the halo center of mass. The time-dependent m=1
perturbation on the disc by the above mechanism correlates with the excitation
of new incidents of non-axisymmetric activity beyond the bar. At every new
excitation, the manifolds act as dynamical avenues attracting particles which
are directed far from corotation along chaotic orbits. The fact that the
manifolds evolve morphologically in time, due to varying non-axisymmetric
perturbations, allows to reconcile manifolds with the presence of multiple
patterns and frequencies in the disc. We find a time-oscillating pattern speed
profile $\Omega_p(R)$ at distances R between the bar's corotation, at resonance
with the succession of minima and maxima of the non-axisymmetric activity
beyond the bar. Finally, we discuss disc thermalization, i.e., the evolution of
the disc velocity dispersion profile and its connection with disc
responsiveness to manifold spirals.
