Although Golubitsky, who came to UH in August 1983, has taught a variety of mathematics courses at the undergraduate and graduate levels, bifurcation theory is his specialty. Bifurcation theory is part of differential equations and addresses how solutions to equations change when a parameter is varied, i.e. the buckling of a beam. When pressure is applied to the ends of a plastic ruler it starts to bend. That change is bifurcation. Recently, people have come to realize that more complicated motions will occur as the system continues to change.
More complicated motion is, for example, a periodic motion like the moon going around the earth.
It seems at first a regular periodic motion, Golubitsky says. The motion is slightly more complicated than that, but it is a regular describable motion. Then there are motions so complicated that there are no easy mathematical descriptions of them. They are called chaotic. Chaos is very complicated motion.