论文标题
表面上强磁系统的正常形式：诱捕区域和ZOLL系统的刚度
Normal forms for strong magnetic systems on surfaces: Trapping regions and rigidity of Zoll systems
论文作者
论文摘要
我们证明了在封闭的，定向表面上强磁场的正常形式，并使用它来得出相关流动的两个动态结果。首先，我们显示了KAM Tori的存在，并且捕获区域提供了一种自然的非共振条件。其次，我们证明该流量不能是ZOLL，除非（i）Riemannian公制具有恒定的曲率并且磁函数是恒定的，或者（ii）磁函数消失并且度量是zoll。我们通过在扁平的两道螺道上表现出外来磁场来补充第二个结果，该磁场可用于任意缩放的Zoll流量。
We prove a normal form for strong magnetic fields on a closed, oriented surface and use it to derive two dynamical results for the associated flow. First, we show the existence of KAM tori and trapping regions provided a natural non-resonance condition holds. Second, we prove that the flow cannot be Zoll unless (i) the Riemannian metric has constant curvature and the magnetic function is constant, or (ii) the magnetic function vanishes and the metric is Zoll. We complement the second result by exhibiting an exotic magnetic field on a flat two-torus yielding a Zoll flow for arbitrarily small rescalings.
