Week 11

I have marked your homework. You can pick up your work from me during the 2nd week of January. I expect the marks to be online any time soon. I have also updated the solutions to the assessed homework online. Note that I have also corrected some of the homework questions. Please do not hesitate to contact me if you think there is still anything left to improve with homework questions and posted answers. Also note the end of Jan deadline for solutions to other homework questions. I hope we will achieve a full set of answers to homework questions!

Towards the end of January I will post instructions on how to study for the exam.

I enjoyed teaching this course to you; I hope the pleasure was mutual. Have a good Xmas and NY break!

Week 10

Please note that next week there will be NO LECTURE ON WED 12 DEC. The lecture on thursday 13 December, 9-11am, will be given by Dr Luzzatto.

Week 9

I was made aware of the fact that in question 4 of Problem Sheet 3, it should be added that the circle map is considered to be orientation preserving. Also the expression for the rotation number was obviously erroneous. I have amended the problem sheet accordingly.

I have also posted the Advanced Coursework for M4/MSc. Hand in deadline is Jan 21, noon. Please consult the attached notes (only one supplied at the moment; the other follow early next week). You are not required to use those, but I thought it may help to give you somewhere to get started.

Week 8

I have posted the answers to the assessed coursework of Problem Sheet 1. I have also handed out Problem Sheet 3, with hand-in deadline of Monday 3 Dec.

Week 6

I handed out Example Sheet nr 2. Please note that the hand-in deadline is monday 19 Nov, noon.

One of you has asked me about homework solutions. I have decided the following:

• all solutions for the assessed questions will appear on this website
• I will be happy to receive from you SERIOUS ATTEMPTS (nearly perfect answers) for all other homework questions. Once I receive such, I will post a model answers on this website. Deadline for submission of answers to non-assessed homework questions will be February 1, 2008.
  

For some of the ambitious ones among you this may be an excellent way to master the course material. Alternatively, you could also coordinate to divide the work load. Good luck!

Week 5

Unfortunately there were a few typos in question 8 of the first exercise sheet, which is part of the assesed coursework. I have now corrected this on the problem sheet that you can download on these pages.

I got a few questions from students about whether a certain kind of answers for the assessed coursework would be "acceptable". Let me assure you here that I am not looking for any specific type of answers. The problems are meant to help you think about the course material (and I will be looking in your answers in signs for this) and not to train you to routinely produce certain specific types of "correct answers".

If you found that you learned something about the course from doing the assessed coursework, I hope it will illustrate you the use of doing exercises to better understand things, and that this will motivate you to try doing the other problems as well... good luck! Also, in the books I recommended earlier you can find additional exercises.

Week 4

Wikepedia has some more on Newton’s method and the related Newton fractal.

I have given out exercise sheet nr 1. Some of the exercises are assessed coursework which need to be handed in before monday 5 nov, noon.

Week 3

You may want to consult these notes on the Jordan Normal Form .

Week 2

If you want to read more about Henri Poincaré, see for instance On the life and work of Henri Poincare, and his prize winning essay.

I used Chaos and Fractals:Understanding the predictable (lecture notes by Michael Thompson, 2005) for some illustrations. You may be interested to have a closer look at these webpages.

Welcome to the course

M3A23/M4A23

INTRODUCTION TO CHAOS

Prof Jeroen S.W. Lamb

Autumn 2007

Lectures: room 140 (Huxley), wednesday 9-10am, thursday 9-11am

The aim of this course is to provide an introduction to basic concepts and ideas underlying the modern qualitative theory of ordinary differential equations (dynamical systems), also popularly known as Chaos Theory.

Suggested literature:

Main text: Boris Hasselblatt and Anatole Katok. A first course in Dynamics. 2003. (textbook)

Other:

Michael Brin and Garrett Stuck. Introduction to Dynamical Systems. 2002. (advanced textbook, recommended buy for the seriously interested)

John Guckenheimer and Philip Holmes. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. 1983. (somewhat dated but inspiring in scope and context)

Anatole Katok and Boris Hasselblatt. Introduction to the Modern Theory of Dynamical Systems.1995. (reference text)

Clark Robinson. Dynamical Systems. Stability, Symbolic Dynamics and Chaos. 1995. (advanced textbook)