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

Abstract : 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.
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Submitted on : Tuesday, April 26, 2011 - 2:59:36 PM
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Marie-Claude Arnaud. A non-differentiable essential irrational invariant curve for a $C^1$ symplectic twist map. Journal of modern dynamics, American Institute of Mathematical Sciences, 2011, 5 (3), pp.583-591. ⟨10.3934/jmd.2011.5.583⟩. ⟨hal-00588781⟩

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