A New Mechanism for Noncollision Singularities

TL;DR

This paper demonstrates the existence of noncollision singularities in a planar four-body problem with a novel model allowing arbitrarily fast acceleration and comparable masses, advancing understanding of complex gravitational dynamics.

Contribution

It introduces a new model for the four-body problem that proves the existence of noncollision singularities, addressing previous open questions and conjectures.

Findings

Proves existence of noncollision singularities in a new four-body model

Provides a general principle for constructing complex orbits

Solves an open question and an analogous conjecture in celestial mechanics

Abstract

In this paper, we prove the existence of noncollision singularities in a planar four-body problem in a model different from [J. Xue,Acta Math.V224(2)253-388, 2020.]. In this model, the acceleration can be arbitrarily fast and the masses can be comparable. This work provides a general principle to construct noncollision singularities as well as other related orbits with complicited dynamics. It not only answers a question in [J. Xue,Acta Math.V224(2) 253-388, 2020.] but also solves an analogous version of a conjecture of Anosov.