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)