The Restricted Three-Body Problem and Holomorphic Curves (Pathways in Mathematics) - Hardcover

Frauenfelder, Urs; Van Koert, Otto

Hardcover

ISBN 10: 3319722778 ISBN 13: 9783319722771

Publisher: Birkhäuser, 2018

Synopsis

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

About this title

From the Back Cover

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 resultsfor 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.

Edition details

• Publisher: Birkhäuser
• Publication date: 2018
• Language: English
• ISBN 10: 3319722778
• ISBN 13: 9783319722771
• Binding: Hardcover
• Edition number: 1
• Number of pages: 385