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A nondifferentiable essential irrational invariant curve for a $C^1$ symplectic twist map

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  • We construct a $C^1$ symplectic twist map $f$ of the annulus that has an essential invariant curve $\Gamma$ such that:
        •$\Gamma$ is not differentiable;
        •$f$ ↾ $\Gamma$ is conjugate to a Denjoy counterexample.
    Mathematics Subject Classification: Primary: 37E40; Secondary: 37E10.


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