非周期性受迫力学系统中不变流形、吸引子和广义KAM环面的检测
Detecting invariant manifolds, attractors, and generalized KAM tori in aperiodically forced mechanical systems
摘要：
我们展示了最近发展的流体流动的测地线传输障碍理论可以用来揭示外部强迫，一个自由度的机械系统中的关键不变流形。具体而言，不变集在这样的系统中变成阴影的柯西-格林应变张量的流动图计算的强制力学系统的最小拉伸测地线。当Poincare映射不可用时，这种方法使得在任意强迫下的广义稳定和不稳定流形、吸引子和广义KAM曲线的有限时间可视化成为可能。我们说明了这些结果的保守和耗散强迫Duffing振子的关键有限时不变集的详细可视化。
英文摘要：
We show how the recently developed theory of geodesic transport barriers for fluid flows can be used to uncover key invariant manifolds in externally forced, one-degree-of-freedom mechanical systems. Specifically, invariant sets in such systems turn out to be shadowed by least-stretching geodesics of the Cauchy-Green strain tensor computed from the flow map of the forced mechanical system. This approach enables the finite-time visualization of generalized stable and unstable manifolds, attractors and generalized KAM curves under arbitrary forcing, when Poincare maps are not available. We illustrate these results by detailed visualizations of the key finite-time invariant sets of conservatively and dissipatively forced Duffing oscillators.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
