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Morse-Smale dense in Diff

  1. Jun 27, 2013 #1
    Hi everybody,

    Taking as a general definition of Morse-Smale (MS) diffeo:

    - finite chain recurrence set
    - Kupka-smale (ie transversalit +hyperbolic periodic points)

    How would you proove that MS is dense and open in Diff(S1)?

    The goal is to have an adapted proof, not use a hammer.

    There is de strien book who asks to:

    Take p in non-wandering set of f.

    - find f1 close to f with p in Per(f1)
    - find f2 with p in Per(f2) and hyperbolic
    - find f3 with p in Per(f3) and all of its periodic points are hyperbolic

    Can you see any logic in this? How would you prove the original statement?

    Thanks for your help! :)
  2. jcsd
  3. Jun 27, 2013 #2
    Any suggestions are most welcome, even if they are incomplete answers...
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