The Restricted Three-Body Problem and Holomorphic Curves

• Main Authors: Frauenfelder, Urs (Author, http://id.loc.gov/vocabulary/relators/aut), van Koert, Otto (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
• Edition: 1st ed. 2018.
• Series: Pathways in Mathematics,
• Subjects: Differential geometry.; Functions of complex variables.; Differential Geometry.; Several Complex Variables and Analytic Spaces.

The book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics. The authors study the restricted three-body problem using recent techniques coming fro...

Table of Contents:

• Introduction
• Symplectic geometry and Hamiltonian mechanics
• Symmetries
• Regularization of two body collisions
• The restricted three body problem
• Contact geometry and the restricted three body problem
• Periodic orbits in Hamiltonian systems
• Periodic orbits in the restricted three body problem
• Global surfaces of section
• The Maslov Index
• Spectral flow
• Convexity
• Finite energy planes
• Siefring's intersection theory for fast finite energy planes
• The moduli space of fast finite energy planes
• Compactness
• Construction of global surfaces of section
• Numerics and dynamics via global surfaces of section.