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

Marie-Claude Arnaud

doi:10.3934/jmd.2011.5.583

Article Contents

2011, Volume 5, Issue 3: 583-591. Doi: 10.3934/jmd.2011.5.583

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

Marie-Claude Arnaud^1,

1.
Université d’Avignon et des Pays de Vaucluse, Laboratoire d’Analyse non linéaire et Géométrie (EA 2151), F-84 018 Avignon

Received: April 2011

Revised: October 2011

Published: November 2011

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Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 37E40; Secondary: 37E10.

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References

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