Symplectic Geometry of Integrable Hamiltonian Systems

1. Auflage 2003
ISBN: 978-3-7643-2167-3
Verlag: Springer

Buch, Englisch, 226 Seiten, Format (B × H): 170 mm x 244 mm, Gewicht: 422 g

Reihe: Advanced Courses in Mathematics - CRM Barcelona

Among all the Hamiltonian systems, the  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).

Zielgruppe

Graduate

Autoren/Hrsg.

Audin, Michèle

Cannas da Silva, Ana

Lerman, Eugene

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Mathematik | Informatik Mathematik Topologie Analytische Topologie
• Mathematik | Informatik Mathematik Geometrie Nicht-Euklidische Geometrie

Inhaltsverzeichnis

A Lagrangian Submanifolds.- I Lagrangian and special Lagrangian immersions in C“.- 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.