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Applied dynamical systems

The field of dynamical systems provides the analytic and geometric methodological framework for the analysis and communication of concepts related to time-evolving systems. Exemplary projects (involving [A, C, S]) are: (a) Simple Eulerian flows can yield complex Lagrangian flows. Ocean currents and eddies provide examples of slowly time dependent flow fields with evident mesoscale structure but chaotic particle trajectories. On the other hand, much sub-surface data from the ocean has a Lagrangian aspect. A critical mathematical question is to understand how much information lies in Lagrangian sub-surface ocean data which is useful for reconstructing the Eulerian flow. This is a data assimilation problem needing significant input from dynamical systems. (b) Novel optical devices such as fiber-guided arrays and new configurations of Bose-Einstein condensates are modelled by systems of nonlinear Schrodinger equations. A critical challenge is to assess the stability of standing waves and other localised structures. Techniques originated in dynamical systems have been effective in providing instability criteria and there is a need to generalise these to higher underlying space dimensions.

Researchers in this area: Baesens, Gelfreich, MacKay, Stuart