Many physical problems, particularly in chemical and biological systems, involve processes that occur on widely varying time scales. The resulting model is a system that has a singular perturbation character. Such problems have motivated the development of much mathematical theory, including classical asymptotic theory and a geometric theory based on invariant manifolds. The phenomena that appear in singular-perturbation problems are subtle, often involving expansions in terms of quantities that are exponentially small in terms of a small parameter in the problem. The singular structure of these equations can also pose formidable numerical challenges. The goal of this workshop was to explore the connection between the asymptotic and geometric theories, with a particular emphasis on exponentially small phenomena, and to bring researchers developing these methods together with people working on applications in biology, chemistry and mechanics.

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1997-1998 Emerging Applications of Dynamical Systems