M3A23/M4A23 Dynamical Systems

This will be about invertible circle maps (see notes on left-hand-side):
[HK] section 4.3 (pages 123-135)
[BS] section 7.1 (pages 153-159)

I will also be available for questions on friday Oct 31 during lunchtime (12pm, Room 638).

I have decided - as an alternative to assessed coursework - to submit you to 3 short progress tests. These tests will take 20 mins at the START of the monday morning lectures (9am SHARP so make sure you are in time (i.e. early)!)

monday 3 November (9.00-9.20am)
monday 17 November (9.00-9.20am)
monday 1 December (9.00-9.20am)

It would be good if all students attending this course have a look through Chapter 3 of the course notes for the 2nd year course M2AA1. The main result discussed there is the contraction mapping theorem and some immediate consequences like the implicit and inverse function theorems. It would be advisable to be familiar with the contraction mapping theorem (in detail inclusive of proof) and with the implicit and inverse function theorems (without proofs).

Videos of pendula and a simulator for the vertically driven pendulum .

Some more more simulators of well known dynamical systems can be found here.

M3A23/M4A23

DYNAMICAL SYSTEMS

Prof Jeroen S.W. Lamb

Autumn 2008

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

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.

This course is strongly recommended for those students intending to take Ergodic Theory (M4A36) and/or Bifurcation Theory (M3A24/M4A23)

Suggested literature:

Main texts:

[BS] Michael Brin and Garrett Stuck. Introduction to Dynamical Systems. 2002. (recommended buy)

[HK] Boris Hasselblatt and Anatole Katok. A first course in Dynamics. 2003.

Other:

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)