Dynamical systems applied to the ocean The ocean is vast and covers almost seventy percent of our planet's surface. Improved predictions of the ocean are, therefore, pivotal in fomulating a better understanding of our planet's climate. Unfortunately, the ocean is an extremely complex chaotic system with the propensity to exhibit sensitive dependence on initial conditions. This has plagued ocean (and more generally weather) forecasting for the last four decades. The work in the group is focussed on two specific aspects that employ dynamical systems ideas to improve our understanding and predictions of the ocean. Our first primary interest is in Lagrangian data assimilation that aims to improve forecasts of the ocean through the use of Lagrangian meters. Examples of such meters include drifters and floats although more exotic instruments such as gliders also fall within this category. Our primary aim here is to combine model forecasts and measurements of Lagrangian meters in an optimum way. The ultimate goal is to develop a mathematical framework for ocean forecasting that would circumvent the problems that are intrinsic to the systems's sensitive dependence on initial conditions. This venture on Lagrangian data assimilation is being pursued with colleagues at the Department of Atmospheric Sciences at UCLA. A second line of work that is of interest to the group is in the application of dynamical systems tools to explain and quanity transport in the ocean. The transport mechanisms in the ocean turn out to be far more complex than what may initially appear possible. However, by using a heirarchy of different flow models, we have been able to explain how Lagrangian chaos can enhance transport within models of the north Atlantic. The dynamical systems methods we have employed rely on the exraction of a set of repelling/ attracting material lines (that are generalisations of stable and unstable manifolds). We have developed a set of numerical tools within the group that allows us to extract and analyse the tranport properties introduced by these flow structures. These ideas are now being combined with Lagrangian data assimilation to provide a unified dynamical systems framework for ocean predictions.