The Restricted Three-Body Problem and Holomorphic Curves (Paperback, Softcover reprint of the original 1st ed. 2018)

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. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Series:	Pathways in Mathematics
Release date:	2019
First published:	2018
Authors:	Urs Frauenfelder • Otto Van Koert
Dimensions:	235 x 155 x 20mm (L x W x T)
Format:	Paperback
Pages:	374
Edition:	Softcover reprint of the original 1st ed. 2018
ISBN-13:	978-3-03-010180-0
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry Promotions
LSN:	3-03-010180-0
Barcode:	9783030101800

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