In case you were wondering, my undergraduate physics thesis was in the area
of quantum chaos, and my advisor was Michel Baranger. I explored the
semiclassical connections between the quantum and classical regimes
in chaotic systems. Specifically, the
device that I used to examine the behavior of these systems is the energy vs. period plot (which is usually
defined classically, but a quantal analogue to it exists). I derived a
semiclassical approximation for it in terms of the classical periodic orbits and then verified my formula
numerically. If you are really interested, my entire thesis is now on the web, equations and figures and all!
There are many links to
chaos-related sites on the Web. For example, here is
a collection of fractal images.