论文标题
环绕环上的保守扭曲地图的不稳定区域的扭转
Torsion of instability zones for conservative twist maps on the annulus
论文作者
论文摘要
对于保留Lebesgue度量的环的扭曲图$ f $，我们提供了足够的条件，以确保存在一组非零渐近扭转点的积极度量。特别是，我们推断出每个有限制的不稳定性区域$ f $都包含一组非零渐近扭转点的积极度量。此外，对于精确的符号扭曲地图$ f $，我们提供了Cheng and Sun的简单，几何证明（请参阅[CS96]），该结果表征了$ \ Mathcal {C}^0 $ - 积分性$ f $的$ f $，而没有共轭点。
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.
