General
This course is part of the MAGIC core.
Description
The course provides an introduction to the topological dynamics of iterated maps: circle maps, unimodal maps, Smale's horseshoe, Hyperbolic toral automorphisms, and polynomials C → C. There is an emphasis on symbolic techniques (kneading theory, Markov partitions, etc.)
The aim is to provide an introduction to a broad range of topics, rather than to discuss any of the topics in great depth.
Semester
Spring 2012 (Monday, January 16 to Friday, March 23)
Timetable- Fri 09:05 - 09:55
Students
|
Abeer AL-NAHDI
(Leeds) |
Nada Alhabib
(Liverpool) |
Michael Bennett
(Cardiff) |
Nasser Bin Turki
(Liverpool) |
|
Yumi Boote
(Manchester) |
Anthony Chiu
(Manchester) |
Mariano Galvagno
(Loughborough) |
Alena Jassova
(Liverpool) |
|
Youssef Lazar
(East Anglia) |
Poj Lertchoosakul
(Liverpool) |
Liangang Ma
(Liverpool) |
Ummu Atiqah Mohd Roslan
(Exeter) |
|
Adam Newman
(Loughborough) |
Robert Pattinson
(Newcastle) |
Jeevan Rai
(Surrey) |
Heather Riley
(Liverpool) |
|
Robert Royals
(East Anglia) |
Francesca Sage-Ling
(Surrey) |
James Wright
(Surrey) |
Stefanie Zegowitz
(East Anglia) |
Prerequisites
Undergraduate-level courses in metric spaces and complex analysis.
Syllabus
- One-dimensional maps, circle maps, logistic map, period doubling cascade
- Chaos, symbolic coding of trajectories
- Two or higher dimensional maps, examples: cat map
- Hyperbolicity, homoclinic intersections, Smale horseshoe
- Quadratic polynomials, Julia and Mandelbrot sets
Bibliography
Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will see links to places where you can buy the book. There is also link marked 'Find this book in a library'. This sometimes works well, but not always. (You will need to enter your location, but it will be saved after you do that for the first time.)
Assessment
Assessment will be by a take home exam at the end of the course. Further details will be provided in due course.
Assignments
MAGIC060 Exam
| Files: | Exam paper | ||
| Deadline: | Friday 27 April 2012 (391.4 days ago) | ||
| Instructions: | The questions are a combination of
Note that you may find the exercises and their solutions helpful, as well as your lecture notes. Good luck! | ||
Files
Files marked L are intended to be displayed on the main screen during lectures.