Critical homoclinics in a restricted four body problem: numerical continuation and center manifold computations

TL;DR

This paper investigates the stability and bifurcations of homoclinic orbits in a restricted four-body problem using numerical continuation and center manifold computations, revealing complex dynamical behaviors.

Contribution

It introduces combined numerical and analytical methods to analyze homoclinic motions and their bifurcations in a four-body celestial system.

Findings

Identification of robust homoclinic orbits

Formulation of conjectures on global bifurcations

Numerical characterization of center manifolds

Abstract

The present work studies the robustness of certain basic homoclinic motions in an equilateral restricted four body problem. The problem can be viewed as a two parameter family of conservative autonomous vector fields. The main tools are numerical continuation techniques for homoclinic and periodic orbits, as well as formal series methods for computing normal forms and center stable/unstable manifold parameterizations. After careful numerical study of a number of special cases we formulate several conjectures about the global bifurcations of the homoclinic families.