Narrow rings: A scattering billiard model

We propose a generic mechanism for the formation of narrow rings in rotatin g systems. For this purpose we use a system of discs rotating about a commo n center lying well outside the discs. a discussion of this system shows th at narrow rings occur, if we assume non-interacting particles. A saddle-cen ter bifurcation is responsible for the relevant appearance of elliptic regi ons in phase space, that will generally assume ring shapes in the synodic f rame, which will suffer a precession in the sidereal frame. Finally we disc uss possible applications of this mechanism and find that it may be relevan t for planetary rings as well as for semiclassical considerations.