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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
[...]
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
[...]
Book combines modern symplectic geometry with the classical three-body problem,
It is an excellent introduction to holomorphic curves in symplectic manifolds, focusing in the case of four-dimensional symplectizations and symplectic cobordisms
It is currently the only book of this kind
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.
| Erscheinungsjahr: | 2018 |
|---|---|
| Fachbereich: | Geometrie |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Reihe: | Pathways in Mathematics |
| Inhalt: |
xi
374 S. |
| ISBN-13: | 9783319722771 |
| ISBN-10: | 3319722778 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-72277-1 |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: |
Koert, Otto van
Frauenfelder, Urs |
| Auflage: | 1st ed. 2018 |
| Hersteller: |
Springer International Publishing
Springer International Publishing AG Pathways in Mathematics |
| Maße: | 241 x 160 x 27 mm |
| Von/Mit: | Otto van Koert (u. a.) |
| Erscheinungsdatum: | 06.09.2018 |
| Gewicht: | 0,746 kg |
Book combines modern symplectic geometry with the classical three-body problem,
It is an excellent introduction to holomorphic curves in symplectic manifolds, focusing in the case of four-dimensional symplectizations and symplectic cobordisms
It is currently the only book of this kind
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.
| Erscheinungsjahr: | 2018 |
|---|---|
| Fachbereich: | Geometrie |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Reihe: | Pathways in Mathematics |
| Inhalt: |
xi
374 S. |
| ISBN-13: | 9783319722771 |
| ISBN-10: | 3319722778 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-319-72277-1 |
| Ausstattung / Beilage: | HC runder Rücken kaschiert |
| Einband: | Gebunden |
| Autor: |
Koert, Otto van
Frauenfelder, Urs |
| Auflage: | 1st ed. 2018 |
| Hersteller: |
Springer International Publishing
Springer International Publishing AG Pathways in Mathematics |
| Maße: | 241 x 160 x 27 mm |
| Von/Mit: | Otto van Koert (u. a.) |
| Erscheinungsdatum: | 06.09.2018 |
| Gewicht: | 0,746 kg |
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