Symplectic Geometry of Integrable Hamiltonian Systems

Michèle Audin, Ana Cannas da Silva, Eugene Lerman

Research output: Book/Report/Conference proceedingBook


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).
Original languageEnglish (US)
PublisherBirkhauser Verlag Basel
Number of pages226
ISBN (Electronic)978-3-0348-8071-8
ISBN (Print)978-3-7643-2167-3
StatePublished - 2003

Publication series

NameAdvanced Courses in Mathematics. CRM Barcelona
PublisherBirkhäuser Verlag, Basel


  • Differential Geometry
  • symplectic geometry
  • manifold
  • contact geometry
  • Integrable Systems


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