论文标题
Birkhoff的平均值和旋转不变的圆圈，用于保护区域地图
Birkhoff Averages and Rotational Invariant Circles for Area-Preserving Maps
论文作者
论文摘要
保护区域图的旋转不变圆是KAM Tori的重要典范。约翰·格林（John Greene）猜想，本地最坚固的旋转圆的旋转数是高尚的，即，持续的分数带有尾巴，并且在这些圆圈中，最坚固的圆形具有金色的平均旋转数。这些猜想的准确数值确认依赖于具有时间逆转对称性的地图，并且这些方法不能应用于更通用的地图。在本文中，我们开发了一种基于加权的Birkhoff平均值来识别不依赖这些对称性的混乱轨道，岛链和旋转不变圆的方法。我们使用Chirikov的标准地图作为测试案例，还证明我们的方法适用于其他三个良好的案例。
Rotational invariant circles of area-preserving maps are an important and well-studied example of KAM tori. John Greene conjectured that the locally most robust rotational circles have rotation numbers that are noble, i.e., have continued fractions with a tail of ones, and that, of these circles, the most robust has golden mean rotation number. The accurate numerical confirmation of these conjectures relies on the map having a time reversal symmetry, and these methods cannot be applied to more general maps. In this paper, we develop a method based on a weighted Birkhoff average for identifying chaotic orbits, island chains, and rotational invariant circles that do not rely on these symmetries. We use Chirikov's standard map as our test case, and also demonstrate that our methods apply to three other, well-studied cases.
