Numerical Analysis of Bifurcation Problems

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My main research interest is the development, analysis, implementation, and application of numerical methods for analyzing the solution behavior of dynamical systems. My work is motivated by the fascinating changes of behavior exhibited by solutions to such equations as parameters are varied: there is tremendous satisfaction in devising new numerical algorithms that help increase our understanding of these phenomena. My recent research includes the determination of so-called invariant manifolds in the famous Lorenz equations, and especially the topological changes of these manifolds as parameter values enter the chaotic regime. Another study concerns the determination of stable and unstable manifolds of periodic orbits in the circular restricted 3-body problem, as these are of great current interest in the design of low-cost orbit transfers in space mission design. Also of practical interest is the analysis of laser models, several of which predict the qualitative and even quantitative behavior of actual physical experiments very well.