Syllabus for Math 5535 --- Fall 2016


This is a one semester course in dynamical systems theory devoted mostly to the study of iteration of mappings of dimension one and two. Most of the basic ideas of dynamical systems theory can be introduced in this setting. Topics to be covered include fixed points, periodic points, stability, bifurcations, conjugacies, chaos, symbolic dynamics, stable manifold theorem, Smale's horseshoe map, fractal dimension, iterated function systems. Many ideas from topology and analysis will be introduced on the way.


Introduction to Dynamical Systems, Continuous and Discrete (2nd edition), by R. Clark Robinson. We will cover much, but not all, of the second half of the book: chapters 8, 9, 10 and parts of chapters 11, 12, 13, 14. The lectures will differ somewhat from the text however.


There will be grades for homework and three midterm exams, weighted as follows:

Homework 25 %
Midterm Exams (25 % each) 75 %

All exams and quizzes are open book/notes, calculators allowed. For a general university policy statement about grades, academic honesty and workload, go to: University Policy Statement.

Exam Dates:

 Midterm I Monday, October 5
 Midterm II Wednesday, November 9
 Midterm III Wednesday, December 14


Homework assignments will be posted on the course website. The first half of the class on most Monday's will be devoted to problem sessions. We will break up into small groups to discuss homework problems from the previous week and do some presentations at the board. I will help out if necessary. In addition, you will have to write up solutions to some of the problems to be graded. To see the assignments as they become available, click on the link above.


Computer experiments can give a lot of insight about dynamical systems. I will present some computer demonstrations in class using the software Mathematica. A Mathematica notebook with some of these demonstrations will be available for download on the course website. You are encouraged to use Mathematica or some other program to do some explorations of your own. You can use Mathematica at the CSE computer labs. To get a CSE computer account go to CSE Accounts. Once you have a CSE lab account, you can also download a copy for your personal computer at: Get Mathematica

Mathematica Notebook:

Here is a Mathematica notebook which will allow you to produce plots like those presented in class. You can easily modify the commands to make similar plots for other dynamical systems. More functions will be added as the semester goes on.

Approximate Schedule:

Here is very tentative week by week outline of the course. This may change as the semester goes on.

 Week  Topic Reading
9/7 Iteration, fixed points, periodic points 8.1, 9.1
9/12-9/14 Graphical iterateion. Stability. Basis of Attraction. 9.2,9.3
9/19-9/21 Singer's theorem, Bifurcations 9.4,9.5
9/28-9/30 More bifurcations, conjugacies 9.5,9.6
10/3-10/5 Review, Midterm I
10/10-10/12 Transition graphs, topological transitivity 10.1,10.2
10/17-10/19 Shift map, itineraries, sensitive dependence 10.3,10.4
10/24-10/26 Invariant Cantor sets 10.5
10/30-11/2 Subshifts 10.6
11/7-11/9 Review, Midterm II
11/14-11/16 Higher dimensional maps, Periodic points 12.1,12.2
11/21-11/23 Stable manifolds, toral automorphisms 12.3, 12.4
11/30-12/2 Horseshoe map, Fractal dimension 13.1,14.1
12/5-12/7 Iterated function systems 14.3
12/12-12/14 Review, Midterm III