Choreography solutions of the $n$-body problem on $S^2$

Abstract

We try to prove the existence of choreography solutions for the $n-$body problem on $S^2$. For the three-body problem, we show the existence of the 8-shape orbit on $S^2$.

References in corpus (4)

• An intrinsic approach in the curved n-body problem: the negative curvature case
• On the stability of tetrahedral relative equilibria in the positively curved 4-body problem
• Classification and stability of relative equilibria for the two-body problem in the hyperbolic space of dimension 2
• The classical N-body problem in the context of curved space

Cited by in corpus (2)

• Equal masses results for choreographies $n$-body problems
• Positive elliptic-elliptic rotopulsators on Clifford tori of nonconstant size project onto regular polygons