  The statistics of Poincar\'e recurrence times in Hamiltonian systems
typically shows a power-law decay with chaotic trajectories sticking to some
phase-space regions for long times. For higher-dimensional systems the
mechanism of this power-law trapping is still unknown. We investigate trapped
orbits of a generic 4D symplectic map in phase space and frequency space and
find that, in contrast to 2D maps, the trapping is (i) not due to a hierarchy
in phase space. Instead, it occurs at the surface of the regular region, (ii)
outside of the Arnold web. The chaotic dynamics in this sticky region is (iii)
dominated by resonance channels which reach far into the chaotic region: We
observe (iii.a) clear signatures of some kind of partial transport barriers and
conjecture (iii.b) a stochastic process with an effective drift along resonance
channels. These two processes lay the basis for a future understanding of the
mechanism of power-law trapping in higher-dimensional systems.
