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Symplectic Geometry of Integrable Hamiltonian Systems

  • Michèle Audin
  • Ana Cannas da Silva
  • Eugene Lerman

Part of the Advanced Courses in Mathematics CRM Barcelona book series (ACMBIRK)

Table of contents

  1. Front Matter
    Pages i-x
  2. Lagrangian Submanifolds

    1. Front Matter
      Pages 1-1
    2. Michèle Audin, Ana Cannas da Silva, Eugene Lerman
      Pages 3-3
    3. Michèle Audin, Ana Cannas da Silva, Eugene Lerman
      Pages 5-48
    4. Michèle Audin, Ana Cannas da Silva, Eugene Lerman
      Pages 49-83
  3. Symplectic Toric Manifolds

    1. Front Matter
      Pages 85-88
    2. Michèle Audin, Ana Cannas da Silva, Eugene Lerman
      Pages 89-127
    3. Michèle Audin, Ana Cannas da Silva, Eugene Lerman
      Pages 129-173
  4. Geodesic Flows and Contact Toric Manifolds

    1. Front Matter
      Pages 175-177
    2. Michèle Audin, Ana Cannas da Silva, Eugene Lerman
      Pages 179-191
    3. Michèle Audin, Ana Cannas da Silva, Eugene Lerman
      Pages 193-195
    4. Michèle Audin, Ana Cannas da Silva, Eugene Lerman
      Pages 197-219
  5. Back Matter
    Pages 221-226

About this book

Introduction

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 Integrable Systems contact geometry manifold symplectic geometry

Authors and affiliations

  • Michèle Audin
    • 1
  • Ana Cannas da Silva
    • 2
  • Eugene Lerman
    • 3
  1. 1.Institut de Recherche Mathématique AvancéeUniversité Louis Pasteur et CNRSStrasbourg CedexFrance
  2. 2.Departamento de MatemáticaInstituto Superior TécnicoLisboaPortugal
  3. 3.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Bibliographic information

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