Global bifurcation of planar and spatial periodic solutions in the restricted n-body problem

TL;DR

This paper investigates the global bifurcation of periodic solutions in the restricted n-body problem, employing orthogonal degree theory to analyze planar and spatial orbits, including special cases like the three-body problem and Maxwell's ring.

Contribution

It introduces a novel application of orthogonal degree to prove global bifurcation of periodic solutions in the restricted n-body problem, covering both planar and spatial cases.

Findings

Established existence of bifurcating periodic solutions from equilibria.

Analyzed specific cases: restricted three-body problem and Maxwell's ring.

Provided conditions under which bifurcations occur.

Abstract

The paper deals with the study of a satellite attracted by n primary bodies, which form a relative equilibrium. We use orthogonal degree to prove global bifurcation of planar and spatial periodic solutions from the equilibria of the satellite. In particular, we analyze the restricted three body problem and the problem of a satellite attracted by the Maxwell's ring relative equilibrium.