Symplectic Geometry of Integrable Hamiltonian Systems

By Eugene Lerman, Michèle Audin, Ana Cannas da Silva

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).

• Format: Paperback
• Language: English
• ISBN: 0817621679
• ISBN13: 9780817621674
• Release Date: March 2004
• Publisher: Birkhauser
• Length: 225 Pages