Advanced Courses in Mathematics - CRM Barcelona

Audin, Michèle; Cannas da Silva, Ana; Lerman, Eugene

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).

Details

Published by: Birkhäuser

Publication Date: 2003-04-24

Format: Paperback

ISBN-13: 9783764321673

DOI: 10.1007/978-3-0348-8071-8

Dimensions: 244cm x170cm

Pages: 226