model answer 3rd test

Please find the model answer here.

topological entropy notes

I am using some selection from [HK] chapter 8 and [BS] sections 2.5 and 2.6

office hours for wed test

monday 12/12 at 12:00 and tuesday 13/12 at 12:00.

third test wed 14/12 09:00-09:30

Material for the third test comprises of [HK] sections 7.3 and 7.4 (with no subsections excluded).For completeness, another link to the a pdf with the relevant material from [HK].

model answer second test

Please find the model answer here.

no strike

Just to let you know class on 30/11 will be as normal 09:00-11:00.

2nd test thursday 24/11 09:00-09:30

The test concerns
[HK 7.1] (not 7.1.2, 7.1.4) and ex. 7.1.1-7.1.10
[HK 7.2] (not 7.2.4) and ex. 7.2.1-7.2.5
[HK 7.3] (not 7.3.3) and ex. 7.3.1-7.3.15

Special office hours (in my office 638 Huxley) are scheduled for this tue 12:00-13:00 and wed 12:00-13:00.

For completeness, another link to the a pdf with the relevant material from [HK].

model answer first test

Please find the model answer here. (apologies for the delay; I had some technical difficulties to overcome due to changing ict infrastructure at college level)

Answers to exercises

Model answers to exercises from the notes and/or problem sheets will be made available if serious attempts to such questions are handed in by any of you, to me or Will. These will then be corrected and model answers published on this website. Please, feel free to work together to maximize the result.

question hour for test

Please note that Will Giles is making himself available for questions 12-1pm on tue 1 Nov, in room 638 Huxley, in view of the test of 2 Nov.

First test Wed 02/11 @ 9:00-9:30am

The first test (of three, total weight 10% of exam) will concern the following material: [HK] section 4.3 and [BS] section 7.1. Relevant problems can be found in these texts, and on the problem sheet (with the exception of questions 3 and 4 on this sheet). The test is there to see if you have understood the material, not whether you learned all the notes by heart (so please do not try to do so). You should be in a good shape if you have studied the notes in detail and are comfortable about the arguments, proofs, etc, and can make some sense of the problems. For a sample test (from 2009) see this link.

The test will start and end on time so please make an effort to arrive well in time.

Circle maps course notes

The course notes for the first chapter consist of [HK] chap 4 (sections 4.3 and 4.4) and [BS] chap 7 (sections 7.1 and 7.2). I followed rather closely [BS] during the lectures, but the material [HK] is essentially identical (but with different presentation).

For associated problems, see the problems in the above-mentioned material, and also the following problem sheet.

Also useful is the [HK] appendix (there appear to be some pages missing, but I will insert these asap), with some useful backgound material.

Please also not the 2009 course website at http://m3a23in2009.blogspot.com.

Welcome to M3/4A23 version 2011

Lectures: room 342 (Huxley), wednesday 9-11am, thurday 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), Bifurcation Theory (M3A24/M4A23) and Advanced Dynamical Systems (M4A38).

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)