Advanced Courses in Mathematics - CRM Barcelona

Symplectic Geometry of Integrable Hamiltonian Systems

Authors: Audin, Michèle, Cannas da Silva, Ana, Lerman, Eugene

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About this Textbook

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).

Reviews

"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


Table of contents (8 chapters)

  • Introduction

    Audin, Michèle (et al.)

    Pages 3-3

  • Lagrangian and special Lagrangian immersions in Cn

    Audin, Michèle (et al.)

    Pages 5-48

  • Lagrangian and special Lagrangian submanifolds in Symplectic and Calabi-Yau manifolds

    Audin, Michèle (et al.)

    Pages 49-83

  • Symplectic Viewpoint

    Audin, Michèle (et al.)

    Pages 89-127

  • Algebraic Viewpoint

    Audin, Michèle (et al.)

    Pages 129-173

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-0348-8071-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-3-7643-2167-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Symplectic Geometry of Integrable Hamiltonian Systems
Authors
Series Title
Advanced Courses in Mathematics - CRM Barcelona
Copyright
2003
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8071-8
DOI
10.1007/978-3-0348-8071-8
Softcover ISBN
978-3-7643-2167-3
Series ISSN
2297-0304
Edition Number
1
Number of Pages
X, 226
Topics