A non-differentiable essential irrational invariant curve for a $C^1$   symplectic twist map
  We construct a $C^1$ symplectic twist map f of the annulus that has an essential invariant curve C such that: --C is not differentiable; -- the dynamic of f restricted to C is conjugated to the one of a Denjoy counter-example. 
Marie-Claude Arnaud (LANLG)
math.DS