Saturn's rings provide a rough example of the center manifold of the tidal forces acting on particles within the rings. Tidal forces have a characteristic "compress and stretch" action on bodies, with the compressing direction defining the stable manifold, the stretching direction defining the unstable manifold, and the neutral direction being the center manifold. In the case of Saturn, a particle in orbit above or below the rings will cross the rings, and, from the viewpoint of the rings, it will appear to oscillate from above to below the plane and back. Thus, it appears that the rings are "attractive". Friction, via collisions with other particles in the rings, will dampen those oscillations; thus they will decrease. Such converging trajectories are characteristic of the stable manifold: particles in the stable manifold come closer together. Particles within the ring will have an orbital radius that is a random walk: as they meet in close encounters with other particles in the ring, they will exchange energy in those encounters, and thus alter their radius. In this sense, the space where the rings lie is neutral: there are no further forces upwards or downwards (out of the plane of the rings), nor inwards or outwards (changing the radius within the rings).