Nonlinear dynamical systems often produce complicated behavior, both temporally and spatially. At least on the level of mathematics, this complicated behavior can occur at all scales both in phase space and in parameter space. Somewhat paradoxically, this points to the need for a coherent set of mathematical techniques that is capable of extracting coarse robust information about specific systems. I believe that topology provides an appropriate language for dealing with these issues. This has motivated my work on the Conley index theory and associated computational methods. The long term goal is to develop general mathematical techniques which are useful in addressing mathematical problems arising from applications. I have a particular interest in applying these techniques to problems arising from mathematical biology.
Last Modified on July 14, 2004
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