Symplectic Geometry of Integrable Hamiltonian Systems (Advanced Courses in Mathematics - CRM Barcelona) - Softcover

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

Softcover

ISBN 10: 3764321679 ISBN 13: 9783764321673

Publisher: Birkhäuser, 2003

Synopsis

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).

About this title

Product Description

Among all the Hamiltonian systems, the integrable ones have special geometric properties; in particular, their solutions are very regular and quasi-periodic. This book serves as an introduction to symplectic and contact geometry for graduate students, exploring the underlying geometry of integrable Hamiltonian systems. Includes exercises designed to complement the expositiont, and up-to-date references.

Review

"This book, an expanded version of the lectures delivered by the authors at the 'Centre de Recerca Matemàtica' Barcelona in July 2001, is designed for a modern introduction to symplectic and contact geometry to graduate students. It can also be useful to research mathematicians interested in integrable systems. The text includes up-to-date references, and has three parts. The first part, by Michèle Audin, contains an introduction to Lagrangian and special Lagrangian submanifolds in symplectic and Calabi-Yau manifolds.... The second part, by Ana Cannas da Silva, provides an elementary introduction to toric manifolds (i.e. smooth toric varieties).... In these first two parts, there are exercises designed to complement the exposition or extend the reader's understanding.... The last part, by Eugene Lerman, is devoted to the topological study of these manifolds."

―ZENTRALBLATT MATH

Edition details

• Publisher: Birkhäuser
• Publication date: 2003
• ISBN 10: 3764321679
• ISBN 13: 9783764321673
• Binding: Paperback
• Language: English
• Number of pages: 236