A family of periodic solutions of the three body problem. Light version

TL;DR

This paper introduces a 1-dimensional family of initial conditions leading to reduced periodic solutions in the three body problem, highlighting bifurcations, symmetries, and numerical validation via the Round Taylor Method.

Contribution

It extends previous periodic solutions by describing a new family with bifurcation points and symmetry properties, supported by numerical error analysis.

Findings

Family contains bifurcation points.

Solutions exhibit different symmetry properties.

Numerical validation confirms solution accuracy.

Abstract

In this paper we describe a 1-dimensional family of initial conditions \Sigma that provides reduced periodic solution of the three body problem. This family \Sigma contains a bifurcation point and extend the periodic solution described in (Perdomo, http://arxiv.org/pdf/1507.01100.pdf). This 1-dimensional family is the union of two embedded smooth curves. We will explain how the trajectories of the bodies in the solutions coming from one of the embedded curves have two symmetries while those coming from the other embedded curve only have one symmetry. The Round Taylor Method is a numerical method implemented by the author to keep track of the global error and the round-off error. A second version of this paper, same title with the "light version" part removed, will include analysis of the error of the solutions using the Round Taylor Method.