Symplectic geometry of integrable Hamiltonian systems / Michèle Audin, Ana Cannas da Silva, Eugene Lerman.

Format:

Book

Author/Creator:

Audin, Michèle.

Contributor:

Silva, Ana Cannas da.

Lerman, Eugene

Ellis D. Williams, College 1865, Endowment Fund.

Series:

Advanced courses in mathematics, CRM Barcelona

Language:

English

Subjects (All):

Hamiltonian systems.

Symplectic manifolds.

Physical Description:

x, 225 pages : illustrations ; 24 cm.

Place of Publication:

Basel ; Boston : Birkhäuser Verlag, 2003.

Summary:

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).

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Ellis D. Williams, College 1865, Endowment Fund.

ISBN:

3764321679

OCLC:

52047311