A non-differentiable essential irrational invariant curve for a $C^1$ symplectic twist map

Marie-Claude Arnaud (1)

1 LANLG - Laboratoire d'Analyse non linéaire et Géométrie

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.

Keywords: twist maps; invariant curves; Denjoy counter-examples

Domains: Dynamical Systems [math.DS]

Marie-Claude Arnaud. A non-differentiable essential irrational invariant curve for a $C^1$ symplectic twist map. Journal of modern dynamics, 2011, 5 (3), pp.583-591. ⟨10.3934/jmd.2011.5.583⟩. ⟨hal-00588781⟩