Regions without invariant tori of given class for the planar circular restricted three-body problem

TL;DR

This paper introduces a method to identify regions in phase space of the planar circular restricted three-body problem that lack invariant tori, with implications for understanding stable planetary orbits around binary stars.

Contribution

The paper develops a novel approach to locate phase space regions without invariant tori, applicable to celestial mechanics and other physical systems.

Findings

Identified regions without invariant tori in the three-body problem

Implications for stable planetary orbits around binary stars

Potential applications to magnetic fields and chemical dynamics

Abstract

A method to establish regions of phase space through which pass no invariant tori transverse to a given direction field is applied to the planar circular restricted three-body problem. Implications for the location of stable orbits for planets around a binary star are deduced. It is expected that lessons learnt from this problem will be useful for applications of the method to other contexts such as flux surfaces for magnetic fields, guiding centre motion in magnetic fields, and classical models of chemical reaction dynamics.