@book{f07fb84c7fb24d49a328affef7adaf44,

title = "Symplectic Geometry of Integrable Hamiltonian Systems",

abstract = "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).",

keywords = "Differential Geometry, symplectic geometry, manifold, contact geometry, Integrable Systems",

author = "Mich{\`e}le Audin and {Cannas da Silva}, Ana and Eugene Lerman",

note = "Lectures delivered at the Euro Summer School held in Barcelona, July 10--15, 2001",

year = "2003",

doi = "10.1007/978-3-0348-8071-8",

language = "English (US)",

isbn = "978-3-7643-2167-3",

series = "Advanced Courses in Mathematics. CRM Barcelona",

publisher = "Birkhauser Verlag Basel",

address = "Switzerland",

}