Existence of hyperbolic motions to a class of Hamiltonians and generalized $N$-body system via a geometric approach

Jiayin Liu, Duokui Yan, Yuan Zhou

For the classical $N$-body problem in ${\mathbb{R}}^d$ with $d\ge 2$, Maderna-Venturelli in their remarkable paper [Ann. Math. 2020] proved the existence of hyperbolic motions with an…