Lecture times: Tuesday 10-11, Friday 12-1.

Venue: John Dedman 1179 (Tuesdays), John Dedman G35 (Fridays).

Workshop times: Mondays 2-5 (to allow 2 hours for most students).

Venue: John Dedman LG104.

Lecturer: Dr. Brian Davies, JD2155.

Course outline: This course aims to give an understanding of regular and chaotic behaviour in non-linear dynamical systems. Some of the lectures will incorporate computer demonstrations using programs which you will also be using. Lectures will commence with a detailed discussion of the iteration of one-dimensional maps, the simplest kind of non-linear dynamical system.This will include analysis of chaotic behaviour, period doubling, intermittent behaviour, and crises. Next will be an introducation to the dynamics of of two-dimensional systems, including the phenomena of fractal structures such as strange attractors and fracally intertwined basins of attraction.Following this, the elementary theory of fractals will be considered. I shall conclude with an introduction to typical behaviour patterns of non-linear differential equations, with an an emphasis on their reduction to the study of maps, as initiated by Henri Poincaré.

Computational content: Apart from attending lectures, there is a major experimental component, using the Computer Laboratories of the Information Commons. Much of the assessment will require independent numerical computation. You will not have to get involved with computer programming to do the computer-based work - all programs will be provided. The Computer Laboratory sessions will also serve as tutorials.

Deadlines for assessable work:

Assignment 3: available Friday August 12th, due date extended to Friday August 26th.

Assignment 6: available Friday September 2nd, due Tuesday September 27th.

Major Project: available Friday September 2nd, due Friday October 21st.

Assignment 8: available Friday October 7th, due date extended to Tuesday October 18th.

It is vital to remember that there is no final examination. The project is worth 50% of the assessment, the other 50% will be taken from the assignments. Deadlines will not be extended except in situations which might qualify for special consideration in final examinations -- ie, inability to organise your personal schedule, etc, will not be accepted as valid grounds.

On-line material:

On-line tutorial (not assessable): a link to on-line material.

Lecture 1 (July 22): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

Lecture 2 (July 26): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

Lecture 3 (July 29): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

Assignment 1 (not assessable): for week commencing August 1.

Lecture 4 (August 2): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

Lecture 5 (August 5): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

Assignment 2 (not assessable): for week commencing August 8.

Lecture 6 (August 9): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

Lecture 7 (August 12): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

Assignment 3 (due date extended to Friday August 26th): click here for some information related to Q3.

Lecture 8 (August 16): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

Lecture 9 (August 19): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

Assignment 4 (not assessable): for week commencing August 22.

Lecture 10 (August 23&26): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

Lecture 11 (August 26&30): notes in pdf form, overheads as "Chaos for Java" files, in zip form.zip form.

Assignment 5 (not assessable): for week commencing August 29.

Lecture 12 (September 2): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

Assignment 6 (due Tuesday September 27).

Major Project (due Friday October 21).

Lecture 13 (September 20): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

Lecture 14 (September 23): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

Assignment 7 (not assessable): for week commencing October 10.

Lecture 15 (September 27): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

Lecture 16 (September 30): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

Assignment 8 (due Tuesday October 18).

Lecture 17 (October 4): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

Lecture 18 (October 7): notes in pdf form.

Lecture 19 (October 11): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

Lecture 20 (October 14): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

Lecture 21 (October 18): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

Lecture 22 (October 21): notes in pdf form, overheads as "Chaos for Java" files, in zip form.

e-mail to Brian.Davies@anu.edu.au
Department of Mathematics
Mathematical Sciences Institute
Australian National University
Canberra ACT 0200
Australia
+61 6 125 2915 (phone)
+61 6 125 4984 (fax)