  The phase--space volume of regions of regular or trapped motion, for bounded
or scattering systems with two degrees of freedom respectively, displays
universal properties. In particular, sudden reductions in the phase-space
volume or gaps are observed at specific values of the parameter which tunes the
dynamics; these locations are approximated by the stability resonances. The
latter are defined by a resonant condition on the stability exponents of a
central linearly stable periodic orbit. We show that, for more than two degrees
of freedom, these resonances can be excited opening up gaps, which effectively
separate and reduce the regions of trapped motion in phase space. Using the
scattering approach to narrow rings and a billiard system as example, we
demonstrate that this mechanism yields rings with two or more components. Arcs
are also obtained, specifically when an additional (mean-motion) resonance
condition is met. We obtain a complete representation of the phase-space volume
occupied by the regions of trapped motion.
