Super-hyperbolic orbits and non-collision singularities in a four-body problem

2023/02/24 by Huang, Guan, Xue, Jinxin
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.12410

Abstract

In this paper, we prove the existence of super-hyperbolic orbits in four-body problem, which solves a conjecture of Marchal-Saari. We also prove the existence of noncollision singularities in the same model, which solves a conjecture of Anosov. Moreover, the two type of solutions coexist for certain mass ratios. We also make a conjecture on the classification of final motions of N-body problem, in which the superhyperbolic type of orbits is one of the building blocks.

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