Next Thursday night (14 Jan) on BBC4 (Freeview) Professor Jim Al-Khalili is doing an hour on chaos theory. The programme is well reviewed and he is one of the bright young things of British physics.
Here's a brief guide to chaos theory:
There are several easy types of stable motion:
1. Staying still.
2. Straight line, constant speed.
3. Regular orbital circular motion.
However, a few years ago it was recognised that there are types of stable motion that are very complex and non-repeating. The big surprise was that it is all based on simple rules. An example is the weather. It goes round and round, doing the same sorts of things at the same times every year, but it never perfectly repeats itself. However, it is a stable system and takes a lot to flip it into a totally new pattern.
Chaos theory is badly named. It is better called "complexity theory".