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