- #1
arpharazon
- 24
- 0
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! :)
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! :)
