Workshop: Coherent Structures in Dynamical Systems; Lorentz Center, Leiden, The Netherlands; 16-20 May 2011

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A proposal has been approved by the Lorentz Center, Leiden, The Netherlands, to carry out a workshop entitled ?Coherent structures in dynamical systems? on 16 May 2011 - 20 May 2011. This NSF support will partially cover the travel cost of US participants in this workshop. The organization of the workshop and substantial part of the cost are provided by the Lorentz Center (http://www.lorentzcenter.nl) .The workshop focus on new collaborations between scientists from different countries and fields, bringing together groups of 30 to 40 junior and senior researchers in a stimulating environment with working space for all participants. Through a combination of informal talks, working sessions, and discussions, participants are able to assess the status of a field and its future, and to collaborate, establish new international contacts, and spot upcoming talent. Central in the study of dynamical systems is the search for invariant sets or coherent structures that organize long-term behavior. Examples of coherent structures include periodic orbits, invariant manifolds, homoclinic orbits, and invariant tori. By performing appropriate local analyses around these coherent structures and studying how they fit together, a "skeleton" of the dynamics may be sketched. In recent years, new techniques have been devised to help unveil dynamical skeletons from limited data sets. These techniques have been mainly applied to unsteady flows in two-space dimensions, leading to a major breakthrough in the physics of mixing; their application to unsteady three-dimensional flows remains largely unexplored. For instance, it remains to be determined if there exists a rigorous theory that can be used as a foundation for coherent structures underlying such flows. An accompanying challenge is the appropriate visualization of coherent structures evolving in three-space dimensions and time. The aim of the workshop, therefore, is to bring together theoretical experts and researchers with interests in the application of dynamical systems methods. Such a gathering is expected to inspire new theoretical research and new areas of application. The workshop will build on the success of the recent Focus Issue on "Lagrangian Coherent Structures in Fluid Flows" in the journal Chaos, which was featured in The New York Times and The Economist. Developing robust methods for uncovering coherent structures in fluid systems will directly influence our ability to make reliable predictions for such high-profile scenarios as the Deepwater Horizon oil spill and the Icelandic volcanic ash cloud, both of which have had tremendous societal impact.