Coherent structures in chaotic dynamical systems (2016–2020)
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. Using transfer operators and state-of-the-art multiplicative ergodic theory as a springboard, this project aims to develop innovative mathematics for bridging these gaps between dynamical systems theory and applications. The intended outcomes include new algorithms for the automatic detection of coherent structures and results about their stability under perturbations.