Journal of Modern Dynamics (JMD)

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

Pages: 583 - 591, Issue 3, July 2011      doi:10.3934/jmd.2011.5.583

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Marie-Claude Arnaud - Université d’Avignon et des Pays de Vaucluse, Laboratoire d’Analyse non linéaire et Géométrie (EA 2151), F-84 018 Avignon, France (email)

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:  Twist maps, invariant curves, irregularity of invariant curves
Mathematics Subject Classification:  Primary: 37E40; Secondary: 37E10.

Received: April 2011;      Revised: October 2011;      Available Online: November 2011.