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

## TL;DR

This paper proves the existence of super-hyperbolic orbits and noncollision singularities in the four-body problem, confirming longstanding conjectures and exploring their coexistence and implications for the classification of N-body motions.

## Contribution

It establishes the existence of super-hyperbolic orbits and noncollision singularities in the four-body problem, solving two major conjectures and analyzing their coexistence.

## Key findings

- Existence of super-hyperbolic orbits in four-body problem
- Existence of noncollision singularities in four-body problem
- Coexistence of both solution types for certain mass ratios

## 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.