Existence of hyperbolic motions to a class of Hamiltonians and
generalized $N$-body system via a geometric approach
Existence of hyperbolic motions to a class of Hamiltonians and
generalized $N$-body system via a geometric approach
For the classical $N$-body problem in $\mathbb{R}^d$ with $d\ge2$, Maderna-Venturelli in their remarkable paper [Ann. Math. 2020] proved the existence of hyperbolic motions with any positive energy constant, starting from any configuration and along any non-collision configuration. Their original proof relies on the long time behavior of solutions by Chazy …