Symplectic Diffeomorphisms

  • Augustin Banyaga
Part of the Mathematics and Its Applications book series (MAIA, volume 400)


Recall that a symplectic form on a 2n-dimensional manifold M is a closed 2-form Ω such that Ω n = Ω Λ Ω Λ ... Λ Ω (n times) is a volume form, i.e. a nowhere vanishing top dimensional differential form. The couple (M, Ω) is called a symplectic manifold, and the volume form Ω n is called the Liouvillie volume of the symplectic manifold (M, Ω).


Open Cover Symplectic Form Symplectic Manifold Lagrangian Submanifold Smooth Family 
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Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Augustin Banyaga
    • 1
  1. 1.Department of MathematicsThe Pennsylvania State UniversityUSA

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