Chaotic Dynamical Systems, Spring 2004

All passed the final!!!

Welcome to the course on Chaotic Dynamical Systems. This web page will provide you with all supplementary course materials, as well as some suggested exercises. In order to read (and print) the posted material, you will need Acrobat Reader (or some equivalent pdf-reader).

AN INTRODUCTION TO CHAOTIC DYNAMICAL SYSTEMS.

By Robert L. Devaney
Paperback: 360 pages ; Dimensions (in inches): 1.25 x 9.25 x 6.25
Publisher: Westview Press; 2nd edition (January 2003)
ISBN: 0813340853

This book is intended for graduate students in mathematics and researchers in other fields who wish to understand more about dynamical systems theory. Half the book is devoted to one-dimensional dynamics, the remainder equally split between higher dimensional dynamics and complex dynamics. The book has been used in undergraduate courses with success. However, it is advisable to cover only the material on one-dimensional dynamics in such a course.

$Devaney$

Note: on Friday, March 5 we meet in room 3513, at 10.15-12.00.

Hand-outs

Schedule
Chaos.pdf (An interesting article concerning Devaney's definition of chaos.)
Thunberg.pdf (A good article about the logistic map, and some of its relatives.)
LiAndYorke.pdf (The classic "Period 3 implies chaos" paper.)
closingLemma.pdf (The improved closing lemma by Pugh.)
broerChaos.pdf (A very nice overview of chaos theory.)
Devaney.pdf (A recent overview of some complex dynamics.)
Shadow.pdf (A short paper on shadowing with good references.)

Suggested exercises

1.2{3}; 1.3{3,4,5,7,8,10}; 1.4{1,2,3,4,6,7}; 1.5{3,4,5}; 1.6{1,2,6}; 1.7{1,2,3}; 1.8{1,5,6,8};
1.9{2,3,4,6,7,9,10,14}; 1.10{2, 3, 4}; 1.11.3; 1.12{1,5,6}; 1.14.1; 1.15{5,7,8}; 2.2{1,3,5,6};
2.3{5,6,7,10}; 2.4.1; 2.5{3,4}; 2.6{2,3,16,17}; 2.8{1,2}.

Homework

(due Friday 30/1) 1.2.3, 1.3{5, 8}, 1.4.1(1-e).
(due Friday 6/2) 1.4.4, 1.5.3, 1.6.6, 1.7.2.
(due Friday 13/2) 1.8.5, 1.9{9, 10}, 1.12.5.
(due Friday 20/2) 1.14.{1, 5}.
(due Friday 27/2) 1.15.{5, 7}, 1.16.{1, 2}.
(due Friday 5/3) 2.2.3; 2.3.{1,7}; 2.4.1.

Software

To run these functions in MATLAB, type 'help cobweb' and/or 'help density' at the MATLAB command promt. This will display enough information to get you up and running.

Old exams

You do not need to do the problems on differential equations or complex dynamics.

Latest edit: 2004-01-22