I'm trying to remember a problem in classical mechanics involving a special surface that allows a ball to roll to the top and lose all it's momentum in finite time.
This leads to some interesting problems with time reversibility, as it implies the ball will spontaneously roll down the surface.
I'm not looking for an explanation, so much as a name and link to study it some more.
I believe the analysis of the Norton Dome is flawed (as many philosophers thought experiments). The ball does not stay at rest and start to move spontaneously in the absence of any force. If there were no forces it will stay there forever. The reason it starts to move is some small perturbations. They could be either external (random variations in pressure around, or just nonisotropic temperature fluctuations; there are plenty of choices). So if you had full information of the system and its surroundings you should be able to predict (in theory, not in practice) which way the ball would move and when. The system is deterministic.
