Semester 1 2003

620-341: Dynamical systems and chaos


Dr. Andrew Rechnitzer
Room = 111 Richard Berry Building
Phone = 8344-8862
Email = andrewr at ms dot unimelb dot edu dot au

I will be away from Friday 9 until Thursday 22 May (inclusive)

Java stuff

While I have not finished this page, some useful java applets from "Exploring Chaos: Theory and Experiment" by Brian Davies can be found here. These applets original come from this page. During the course I will (from time to time) make use of some of these. You maybe expected to make use them for your assignments.

More chaos associated applets can be found here.

A nice fractal generator (that has lots of features) is JAME, which is free to download (thoughyou will need some java stuff installed on your machine). The above pictureswere made with it. After the course you should understand what these pictures actually mean.

Topics covered

The class will (mostly) follow the book: " A First Course in Chaotic Dynamical Systems" by Bob Devaney. While this is a new book on chaos which actually has some mathematical content, you are not expected to buy it for the course.
I will also make use of some material from "Exploring Chaos: Theory and Experiment". Again, you are not expected to buy it.

14th April: Finally there are copies of these two books on the reserve desk in the mathematics library. Enjoy.

I hope to cover all of the following topics (in order?):
  1. A brief history of dynamics and an introduction to chaos
  2. Orbits of functions
  3. Graphical analysis of functions
  4. Fixed and periodic points
  5. Bifurcations
  6. The quadratic family and the logistic function
  7. The period doubling route to chaos
  8. Symbolic dynamics
  9. How to define chaos
  10. Sarkovskii's theorem
  11. Fractals
  12. The Julia set
  13. The Mandelbrot set
If there is time we may cover some other topics....


Contact times and places

Class representative on the SSLC

Generic Skills

During the course you will have the opportunity to acquire some generic skills.

Handouts and other bits and pieces