Global surfaces of section in the planar restricted 3-body problem

TL;DR

This paper proves the existence of a global surface of section near the smaller body in the planar restricted three-body problem for new energy and mass ratio ranges, using modern symplectic geometry methods.

Contribution

It introduces a novel approach based on global symplectic geometry to establish surfaces of section in cases previously inaccessible by perturbative methods.

Findings

Existence of global surfaces of section in new parameter ranges

Application of symplectic geometry techniques to celestial mechanics

Contrasts with traditional perturbative approaches

Abstract

The restricted planar three-body problem has a rich history, yet many unanswered questions still remain. In the present paper we prove the existence of a global surface of section near the smaller body in a new range of energies and mass ratios for which the Hill's region still has three connected components. The approach relies on recent global methods in symplectic geometry and contrasts sharply with the perturbative methods used until now.