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arXiv · 2006.04447

Torsion of instability zones for conservative twist maps on the annulus

Anna Florio·Patrice Le Calvez
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Abstract

For a twist map $f$ of the annulus preserving the Lebesgue measure, we give sufficient conditions to assure the existence of a set of positive measure of points with non-zero asymptotic torsion. In particular, we deduce that every bounded instability region for $f$ contains a set of positive measure of points with non-zero asymptotic torsion. Moreover, for an exact symplectic twist map $f$, we provide a simple, geometric proof of a result by Cheng and Sun (see [CS96]) which characterizes $\mathcal{C}^0$-integrability of $f$ by the absence of conjugate points.

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Anna Florio, Patrice Le Calvez. 2020-06-08. Torsion of instability zones for conservative twist maps on the annulus. https://arxiv.org/abs/2006.04447

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