Global bifurcation of planar and spatial periodic solutions from the polygonal relative equilibria for the n-body problem

TL;DR

This paper investigates the global bifurcation of periodic solutions in the n-body problem, focusing on polygonal configurations with symmetries, using advanced mathematical tools to classify bifurcating branches in planar and spatial cases.

Contribution

It provides a comprehensive analysis of bifurcations from polygonal relative equilibria in the n-body problem, employing symmetry and orthogonal degree theory to identify all bifurcating solution branches.

Findings

Complete bifurcation analysis for regular polygon configurations.

Identification of symmetries and irreducible representations involved.

Classification of bifurcating solutions in both planar and spatial settings.

Abstract

Given $n$ point masses turning in a plane at a constant speed, this paper deals with the global bifurcation of periodic solutions for the masses, in that plane and in space. As a special case, one has a complete study of n identical masses on a regular polygon and a central mass. The symmetries of the problem are used in order to find the irreducible representations, the linearization, and with the help of the orthogonal degree theory, all the symmetries of the bifurcating branches.