Existence of Hyperbolic Orbits for N-body Type Problems

TL;DR

This paper proves the existence of hyperbolic orbits with positive energy in N-body problems using variational methods, starting from periodic solutions and taking limits.

Contribution

It introduces a novel variational approach to establish hyperbolic solutions for N-body problems with strong forces, expanding understanding of their orbital dynamics.

Findings

Existence of hyperbolic orbits with prescribed positive energy.

Construction of hyperbolic solutions via limits of periodic solutions.

Application of variational minimizing method to N-body problems.

Abstract

In this paper, we use variational minimizing method to prove the existence of hyperbolic solution with a prescribed positive energy for N-body type problems with strong forces. Firstly, we get periodic solutions using suitable constraints, then by taking limit about a sequence of periodic solutions, we get the hyperbolic orbits.