Every collision-free limit shape is realized as the exact escape shape of a Newtonian hyperbolic motion from any initial configuration and any positive energy.
Maderna, On weak KAM theory for N-body problems, Ergod
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Viscosity solutions and hyperbolic motions: a new PDE method for the $N$-body problem
Every collision-free limit shape is realized as the exact escape shape of a Newtonian hyperbolic motion from any initial configuration and any positive energy.