Recently I came across the problem of Norton's dome.
I thought of two questions, for which I found no answer.
- Does there exist a newtonian initial value problem, where the total force on each body is non-zero everywhere, with more than one solution and/or broken symmetry?
- Given a newtonian system, is the property of an initial condition to have a unique solution generic?
(i.e. is the subset of initial conditions with a unique solution open and dense?)