Author	Audin, Michรจle. author
Title	Symplectic Geometry of Integrable Hamiltonian Systems [electronic resource] / by Michรจle Audin, Ana Cannas da Silva, Eugene Lerman
Imprint	Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2003
Connect to	http://dx.doi.org/10.1007/978-3-0348-8071-8
Descript	X, 226 p. online resource

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)

A Lagrangian Submanifolds -- I Lagrangian and special Lagrangian immersions in Cโ -- II Lagrangian and special Lagrangian submanifolds in symplectic and Calabi-Yau manifolds -- B Symplectic Toric Manifolds -- I Symplectic Viewpoint -- II Algebraic Viewpoint -- C Geodesic Flows and Contact Toric Manifolds -- I From toric integrable geodesic flows to contact toric manifolds -- II Contact group actions and contact moment maps -- III Proof of Theorem I.38 -- List of Contributors

1. Mathematics
2. Differential geometry
3. Manifolds (Mathematics)
4. Complex manifolds
5. Physics
6. Mathematics
7. Differential Geometry
8. Manifolds and Cell Complexes (incl. Diff.Topology)
9. Mathematical Methods in Physics