论文标题
两个涡流的故事：数值千古理论和转移操作员如何揭示非自治动力学系统中相干结构的基本变化
A tale of two vortices: how numerical ergodic theory and transfer operators reveal fundamental changes to coherent structures in non-autonomous dynamical systems
论文作者
论文摘要
相干结构在空间上是变化的区域，随着时间的流逝，分散并在非自主系统中组织运动。这项工作开发和实施了算法，提供了时间依赖性系统的多层描述，这些描述不仅对定位相干结构有用，还可以检测这些结构经历基本结构变化的时间窗口，例如合并和拆分事件。这些算法依赖于与动态系统引起的转移运算符的ULAM类型离散化相关的奇异价值分解，并基于乘法千古理论的最新发展。此外，它们使我们能够研究相关奇异值分解的演变与系统动力学特征之间的各种联系。该方法在定期和准周期驱动系统的模型以及对应于南极涡流分裂的地球物理数据集上进行了测试。
Coherent structures are spatially varying regions which disperse minimally over time and organise motion in non-autonomous systems. This work develops and implements algorithms providing multilayered descriptions of time-dependent systems which are not only useful for locating coherent structures, but also for detecting time windows within which these structures undergo fundamental structural changes, such as merging and splitting events. These algorithms rely on singular value decompositions associated to Ulam type discretisations of transfer operators induced by dynamical systems, and build on recent developments in multiplicative ergodic theory. Furthermore, they allow us to investigate various connections between the evolution of relevant singular value decompositions and dynamical features of the system. The approach is tested on models of periodically and quasi-periodically driven systems, as well as on a geophysical dataset corresponding to the splitting of the Southern Polar Vortex.
