Bifurcation Theory

Math 689-001

Spring 2018


This is the web page http://math.cos.gmu.edu/~wanner/courses/m689s18/index.html
It will be updated regularly and always contain the latest information on the course.

General Information:

Instructor: Thomas Wanner
Office: Exploratory Hall 4404
E-mail: twanner@gmu.edu
Web Page: http://math.cos.gmu.edu/~wanner/
Fax: (703) 993-1491
Office hours: TR 1pm-2pm, and by appointment

Lectures: TR 10:30-11:45am, Exploratory Hall 4106
Prerequisites: A thorough knowledge of undergraduate advanced calculus, linear algebra, and differential equations is assumed. Also, familiarity with the "Theorem-Proof" style of presentation is important.
Textbook: No required textbook.


Important Links:


Syllabus:

The course introduces basic concepts and techniques of bifurcation theory for discrete and continuous dynamical systems. These include topological equivalence and structural stability of dynamical systems, local bifurcations of equilibria and periodic orbits, normal forms, and global bifurcations. Time permitting, we will also discuss bifurcations in symmetric systems, as well as bifurcation theory geared towards computer-assisted proofs. At least the beginning of the course will follow the book by Yuri Kuznetsov, Elements of Applied Bifurcation Theory, Springer-Verlag. A more detailed syllabus can be found here. It will be updated weekly.


Homework Assignments:

Homework problems will be assigned once a week and posted on Blackboard in the Assignments section. Some of these assignments will be graded and count towards your homework score. While the remaining ones do not have to be handed in, I do advise everyone strongly to study them and write out the solutions properly. I will go through many of the homework problems in the following class and you will not benefit from this if you have not made a serious attempt at solving them.


Grading Policy:

Your final grade in the course will be determined from your performance in the homework assignments, a final project/presentation, and your attendance and class participation. Weights for these items will be distributed approximately according to the following schedule:

Homework Final Project/Presentation Attendance
60% 30% 10%


Thomas Wanner, December 12, 2017.