Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Symplectic Manifolds

  1. Apr 4, 2010 #1
    What's a really good resources with numerous easy-to-follow proofs to theorems on symplectic manifolds?

    Arnold is too difficult.
     
  2. jcsd
  3. Apr 4, 2010 #2

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The most basic book is probably Lectures on Symplectic Geometry by Anna Canna Da Silva.

    The big book about classical machanics by Abraham and Marsden is also basic but of course it only covers stuff pertinent to classical mechanics.

    After that there is Introduction to Symplectic Topology by Salamon and McDuff but this is already more difficult.
     
  4. Apr 5, 2010 #3
    I picked up the one by Marsden, the rest seemed to advanced for me.
     
  5. Apr 5, 2010 #4

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    What is the source of your interest in symplectic geometry? Do you want to learn about the symplectic formulation of mechanics?
     
  6. Apr 5, 2010 #5
    Well I can't follow Arnold so I need a better reference.
     
  7. Apr 5, 2010 #6

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I am just curious which aspects of symplectic geometry you are interested in learning and why.
     
  8. Apr 5, 2010 #7
    Symplectic formualtion of mechanics to answer ur question.

    I need to understand ch. 8 in arnold
     
  9. Apr 5, 2010 #8

    dx

    User Avatar
    Homework Helper
    Gold Member

    Try Walter Thirring's "Classical Dynamical Systems" and Fomenko's "Visual Geometry and Topology" .
     
  10. Apr 5, 2010 #9

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    ok, well good luck with marsden!
     
  11. Apr 7, 2010 #10
    Arnold is as basic as it gets, if you want to understand it mathematically. Understanding the definition of a symplectic manifold requires a good deal of math. Since there's no equivalent definition that doesn't require a lot of heavy math, you may be out of luck.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Symplectic Manifolds
  1. Symplectic geometry (Replies: 2)

Loading...