We construct a $C^2$ symplectic twist map f of the annulus that has an essential invariant curve C such that: - C is not differentiable; - the dynamics of f restricted to C is conjugated to the one of a Denjoy counter-example; - C is at the boundary of an instability zone for f.
A non-differentiable essential irrational invariant curve for a $C^1$ symplectic twist map
Optical Hamiltonians and symplectic twist maps
Non-resonant tori in symplectic twist maps without conjugate points
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