The Restricted Three-Body Problem and Holomorphic Curves
2018 ed.
Book Details
Format
Hardback or Cased Book
Book Series
Pathways in Mathematics
ISBN-10
3319722778
ISBN-13
9783319722771
Edition
2018 ed.
Publisher
Birkhauser Verlag AG
Imprint
Birkhauser Verlag AG
Country of Manufacture
CH
Country of Publication
GB
Publication Date
Sep 6th, 2018
Print length
374 Pages
Weight
738 grams
Dimensions
16.30 x 24.20 x 2.30 cms
Product Classification:
Complex analysis, complex variablesDifferential & Riemannian geometry
Ksh 19,800.00
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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 Geometryhttp://www.springer.com/series/16019
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