双涡旋的故事：数值遍历理论与转移算子如何揭示非自治动力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
AI总结：
本文开发基于转移算子奇异值分解的算法，用于定位非自治系统中的相干结构并检测其合并与分裂等变化，在周期、准周期驱动模型及南极极涡分裂数据上验证。
摘要：
相干结构是随时间变化的空间区域，它们在非自治系统中随时间扩散最小，并组织系统的运动。本文开发并实现了算法，提供对时变系统的多层次描述，这些描述不仅有助于定位相干结构，还能检测这些结构发生根本性变化（如合并和分裂事件）的时间窗口。这些算法依赖于与动力系统诱导的转移算子的Ulam型离散化相关的奇异值分解，并建立在乘法遍历理论的最新进展之上。此外，它们使我们能够研究相关奇异值分解的演化与系统动力学特征之间的各种联系。该方法在周期性和准周期性驱动系统模型上进行了测试，并应用于与南极极涡分裂相关的地球物理数据集。
英文摘要：
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.
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。
