论文标题
通过加权伯克霍夫的平均值区分普通的和混乱的流动轨道
Distinguishing between Regular and Chaotic orbits of Flows by the Weighted Birkhoff Average
论文作者
论文摘要
本文调查了加权Birkhoff平均值（WBA）的效用，以区分定期和混乱的流动轨道，从而扩展了将WBA应用于地图的先前结果。结果表明，当动力学和相空间函数平滑时，WBA可以对流量进行超质量，并且动力学与二磷旋转载体结合到刚性旋转。研究了平均值对轨道长度和重量函数宽度宽度的依赖性。在实践中，平均在O（10^3）周期的集成时间内实现了旋转轨道旋转频率的精确度。混乱轨迹的对比相对较慢的收敛性允许有效的歧视标准。研究了三个示例系统：一个两波哈密顿系统的系统，一种准静脉体强迫，耗散系统，具有一个奇怪的吸引子，没有正lyapunov指数，以及用于磁场线流量的模型。
This paper investigates the utility of the weighted Birkhoff average (WBA) for distinguishing between regular and chaotic orbits of flows, extending previous results that applied the WBA to maps. It is shown that the WBA can be super-convergent for flows when the dynamics and phase space function are smooth, and the dynamics is conjugate to a rigid rotation with Diophantine rotation vector. The dependence of the accuracy of the average on orbit length and width of the weight function width are investigated. In practice, the average achieves machine precision of the rotation frequency of quasiperiodic orbits for an integration time of O(10^3) periods. The contrasting, relatively slow convergence for chaotic trajectories allows an efficient discrimination criterion. Three example systems are studied: a two-wave Hamiltonian system, a quasiperiodically forced, dissipative system that has a strange attractor with no positive Lyapunov exponents, and a model for magnetic field line flow.
