The symplectic geometry of the three-body problem

TL;DR

This paper explores the classical restricted three-body problem using modern symplectic and contact geometry methods, covering theoretical foundations and practical applications like space mission design.

Contribution

It applies advanced symplectic and contact geometric techniques to analyze the three-body problem, bridging theoretical insights with practical astrodynamics.

Findings

Insights into Floer theory and contact topology in celestial mechanics

New approaches to symplectic dynamics relevant for space missions

Enhanced understanding of the three-body problem structure

Abstract

A book, concerning the classical restricted three body problem, and the approach to this old conundrum coming from the modern methods of symplectic and contact geometry. It is split into Part I (theoretical aspects), and Part II (practical aspects). The main themes are Floer theory, contact topology, symplectic dynamics, and astrodynamics (with a view towards space mission design).