Modern mathematics to unravel the birth of coherence in dynamical systems

该项目旨在揭示动力系统中长寿命相干特征出现和消失的精确数学机制。这个项目期望在动力系统领域产生新的基础数学，使用创新的算子理论方法来仔细梳理连贯结构的生命周期。该项目的预期成果包括新的数学理论和计算算法，以预测相干物体的产生和破坏，这些物体是复杂地球物理流动的关键组织者。这一数学上的突破将带来显著的好处，比如改善对涡旋输送的预测以及天气和气候模式的持久性。

This project aims to reveal the precise mathematical mechanisms underlying the emergence and disappearance of long-lived coherent features in dynamical systems. This project expects to generate new fundamental mathematics in the area of dynamical systems, using innovative operator-theoretic approaches to carefully tease apart the lifecycles of coherent structures. The expected outcomes of this project include new mathematical theory and computational algorithms to anticipate the genesis and destruction of coherent objects, which are key organisers of complex geophysical flows. This breakthrough mathematics should provide significant benefits, such as improved prediction of eddy transport and persistence of weather and climate patterns.