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Bibframe Work

Title
The Restricted Three-Body Problem and Holomorphic Curves 4
Type
Text
Monograph
Contribution
Frauenfelder, Urs (author)
van Koert, Otto (author)
Subject
(BISACSH)
Geometry, Differential (LCSH)
Functions of complex variables (LCSH)
Language
English (eng)
Classification
DDC: 516.36 full (Source: 23)
LCC: QA641-670 (Status: not used by assignerprepublication)
Content
text (txt)
Summary
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 from the theory of pseudo-holomorphic curves. The book starts with an introduction to relevant topics in symplectic topology and Hamiltonian dynamics before introducing some well-known systems from celestial mechanics, such as the Kepler problem and the restricted three-body problem. After an overview of different regularizations of these systems, the book continues with a discussion of periodic orbits and global surfaces of section for these and more general systems. The second half of the book is primarily dedicated to developing the theory of holomorphic curves - specifically the theory of fast finite energy planes - to elucidate the proofs of the existence results for global surfaces of section stated earlier. The book closes with a chapter summarizing the results of some numerical experiments related to finding periodic orbits and global surfaces of sections in the restricted three-body problem.
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.
Authorized Access Point
Frauenfelder, Urs. The Restricted Three-Body Problem and Holomorphic Curves
Admin Metadata
Status: new
Date: 2018-08-29
Admin Metadata
Status: changed
Date: 2024-12-26T14:20:40
Admin Metadata
Status: changed
Date: 2025-04-27T00:05:28.579254-04:00
Admin Metadata
Encoding Level: preliminary
Identified By: bf:Local, 21580056
Description Language: English
Note: 040 $aDLC$beng$epn$erda$cDLC

series
Pathways in Mathematics
Pathways in Mathematics
other physical format
The restricted three-body problem and holomorphic curves
The Restricted Three-Body Problem and Holomorphic Curves
The Restricted Three-Body Problem and Holomorphic Curves
The Restricted Three-Body Problem and Holomorphic Curves
Printed edition
The Restricted Three-Body Problem and Holomorphic Curves
The Restricted Three-Body Problem and Holomorphic Curves
The Restricted Three-Body Problem and Holomorphic Curves