The Restricted Three-Body Problem And Holomorphic Curves - Frauenfelder Urs; Van Koert Otto | Libro Birkhäuser 01/2019 - HOEPLI.it


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frauenfelder urs; van koert otto - the restricted three-body problem and holomorphic curves

The Restricted Three-Body Problem and Holomorphic Curves

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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Birkhäuser

Pubblicazione: 01/2019
Edizione: Softcover reprint of the original 1st ed. 2018





Trama

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





Sommario

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.








Altre Informazioni

ISBN:

9783030101800

Condizione: Nuovo
Collana: Pathways in Mathematics
Dimensioni: 235 x 155 mm Ø 593 gr
Formato: Brossura
Pagine Arabe: 374
Pagine Romane: xi






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