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The manifold theory of barred-spiral structure provides a dynamical mechanismexplaining how spiral arms beyond the ends of galactic bars can be supported bychaotic flows extending beyond the bar's co-rotation zone. We discuss itsapplicability to N-body simulations of secularly evolving barred galaxies. Inthese simulations, we observe consecutive `incidents' of spiral activity,leading to a time-varying disc morphology. Besides disc self-excitations, weprovide evidence of a newly noted excitation mechanism related to the`off-centering' effect: particles ejected in elongated orbits at majorincidents cause the disc center-of-mass to recoil and be set in a wobble-typeorbit with respect to the halo center of mass. The time-dependent m=1perturbation on the disc by the above mechanism correlates with the excitationof new incidents of non-axisymmetric activity beyond the bar. At every newexcitation, the manifolds act as dynamical avenues attracting particles whichare directed far from corotation along chaotic orbits. The fact that themanifolds evolve morphologically in time, due to varying non-axisymmetricperturbations, allows to reconcile manifolds with the presence of multiplepatterns and frequencies in the disc. We find a time-oscillating pattern speedprofile $\Omega_p(R)$ at distances R between the bar's corotation, at resonancewith the succession of minima and maxima of the non-axisymmetric activitybeyond the bar. Finally, we discuss disc thermalization, i.e., the evolution ofthe disc velocity dispersion profile and its connection with discresponsiveness to manifold spirals.

Manifold spirals, disc-halo interactions and the secular evolution in N-body models of barred galaxies