The Restricted Three-Body Problem and Holomorphic Curves

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...

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Bibliographische Detailangaben
1. Verfasser: Frauenfelder, Urs (VerfasserIn)
Format: Elektronisch E-Book
Sprache:Englisch
Veröffentlicht: Cham : Springer International Publishing, 2018.
Ausgabe:1st ed. 2018.
Schriftenreihe:Pathways in Mathematics,
Schlagworte:
Differential geometry.
Functions of complex variables.
ISBN:9783319722788
ISSN:2367-3451
Online-Zugang: Volltext
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Inhaltsangabe:
  • 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.

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