Chaotic Dynamical Systems

Chaos arises in mathematics when arbitrarily small changes in initial data can lead to immense changes in results over a fixed time interval. This course studies these phenomena both in the abstract and by experimentally using the computer algebra systems running on the X terminals connected to an IBM RSC/6000 Powerstation. It begins with the iteration of polynomial maps of one real variable. Most important phenomena are already present in this simple situation. The iteration of quadratic functions of one complex variable will lead to the Mandelbrot set.

Fall, Spring, Summer