Symplectic Geometry of Integrable Hamiltonian Systems
Language: English
Published by Birkhäuser, 2003
- Softcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
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Condition: New
US$ 59.53
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Druck auf Anfrage Neuware - Printed after ordering - Among all the Hamiltonian systems, theintegrable ones have special geometric properties; in particular, their solutions are very regular and quasi-periodic. The quasi-periodicity of the solutions of an integrable system is a result of the fact that the system is invariant under a (semi-global) torus action. It is thus natural to investigate the symplectic manifolds that can be endowed with a (global) torus action. This leads to symplectic toric manifolds (Part B of this book). Physics makes a surprising come-back in Part A: to describe Mirror Symmetry, one looks for a special kind of Lagrangian submanifolds and integrable systems, the special Lagrangians. Furthermore, integrable Hamiltonian systems on punctured cotangent bundles are a starting point for the study of contact toric manifolds (Part C of this book).
Seller Inventory # 9783764321673
- Title
- Symplectic Geometry of Integrable Hamiltonian Systems
- Author
- Ana Cannas Da Silva
- Publisher
- Birkhäuser
- Publication year
- 2003
- Condition
- Neu
- Binding
- Taschenbuch
- Language
- English
- ISBN 10
- 3764321679
- ISBN 13
- 9783764321673
- Item weight
- 422 grams
- Dimensions
- 244x170x14 mm
Among all the Hamiltonian systems, the integrable ones have special geometric properties; in particular, their solutions are very regular and quasi-periodic. The quasi-periodicity of the solutions of an integrable system is a result of the fact that the system is invariant under a (semi-global) torus action. It is thus natural to investigate the symplectic manifolds that can be endowed with a (global) torus action. This leads to symplectic toric manifolds (Part B of this book). Physics makes a surprising come-back in Part A: to describe Mirror Symmetry, one looks for a special kind of Lagrangian submanifolds and integrable systems, the special Lagrangians. Furthermore, integrable Hamiltonian systems on punctured cotangent bundles are a starting point for the study of contact toric manifolds (Part C of this book).
"Synopsis" may belong to another edition of this title.
Review
"This book, an expanded version of the lectures delivered by the authors at the 'Centre de Recerca Matemàtica' Barcelona in July 2001, is designed for a modern introduction to symplectic and contact geometry to graduate students. It can also be useful to research mathematicians interested in integrable systems. The text includes up-to-date references, and has three parts. The first part, by Michèle Audin, contains an introduction to Lagrangian and special Lagrangian submanifolds in symplectic and Calabi-Yau manifolds.... The second part, by Ana Cannas da Silva, provides an elementary introduction to toric manifolds (i.e. smooth toric varieties).... In these first two parts, there are exercises designed to complement the exposition or extend the reader's understanding.... The last part, by Eugene Lerman, is devoted to the topological study of these manifolds."
―ZENTRALBLATT MATH
"About the title" may belong to another edition of this title.
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