Coherent structures in chaotic dynamical systems

这个项目以转移算子和最先进的乘法遍历理论为跳板，旨在发展创新的数学，以弥合动力系统理论和应用之间的差距。相干结构，如海洋涡旋和大气涡旋，普遍存在于现实世界的动力系统中，在天气和气候系统中都发挥着至关重要的作用。这些结构出现在外力系统中，而现有的关于它们的位置、数量和对模型误差的稳定性的理论比非强迫系统中的要少得多。预期的成果包括用于自动检测相干结构的新算法以及关于它们在扰动下的稳定性的结果，这些扰动与天气和气候系统中的作用有关。

Using transfer operators and state-of-the-art multiplicative ergodic theory as a springboard, this project aims to develop innovative mathematics for bridging gaps between dynamical systems theory and applications. Coherent structures, such as oceanic eddies and atmospheric vortices, are prevalent in real-world dynamical systems and play a crucial role in both weather and climate systems. These structures arise in externally forced systems, and the existing theory concerning their location, number and stability to model errors is much less understood than in the non-forced counterpart. The intended outcomes include new algorithms for the automatic detection of coherent structures and results about their stability under perturbations which are relevant to roles in both weather and climate systems.