Bifurcations of critical orbits of invariant potentials with applications to bifurcations of central configurations of the N-body problem

TL;DR

This paper investigates topological bifurcations of critical orbits in equivariant gradient equations and applies the findings to bifurcations of central configurations in the N-body problem.

Contribution

It provides necessary and sufficient conditions for global bifurcations of solutions and applies these to new families of planar central configurations.

Findings

Established conditions for global bifurcations of critical orbits

Identified new bifurcation phenomena in N-body central configurations

Extended bifurcation theory to equivariant gradient systems

Abstract

In this article we study topological bifurcations of critical orbits of equivariant gradient equations. We give necessary and sufficient conditions for the existence of global bifurcations of solutions of these equations. Moreover, we apply these abstract results to the study of bifurcations of new families of planar central configurations of the N-body problem.