| Symplectic Geometry of Integrable Hamiltonian Systems 2003 Edition Contributor(s): Audin, Michèle (Author), Cannas Da Silva, Ana (Author), Lerman, Eugene (Author) |
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ISBN: 3764321679 ISBN-13: 9783764321673 Publisher: Birkhauser OUR PRICE: $56.95 Product Type: Paperback - Other Formats Published: April 2003 Annotation: 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). |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Differential - Science | Physics - Mathematical & Computational - Mathematics | Topology - General |
| Dewey: 514.74 |
| LCCN: 2003050032 |
| Series: Advanced Courses in Mathematics: CRM Barcelona |
| Physical Information: 0.51" H x 7" W x 10" (0.93 lbs) 226 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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). |
