MA771 - Discrete Dynamical Systems - Spring
Lectures: MWF 11-12 in PSY B42
Content of Course:
This course is a graduate level introduction to the mathematical theory of discrete dynamical
systems. We will discuss some fundamental examples in the field,
including circle rotations, expanding maps, shifts and subshifts,
quadratic maps, toral automorphisms, the horseshoe, and the
solenoid, and cover topics such as limit sets and recurrence,
topological mixing, transitivity, and entropy, symbolic dynamics,
stable and unstable manifolds, the Hartman-Grobman Theorem, and basic
ergodic theory. (Note: to some extent this is subject to change.)
- Presentations will be held on Friday, April 30, from 10am-4pm in MCS
148. Please make sure you are able to stay and hear everyone's presentation that
day. Lunch will be provided.
Books and references:
This books is not yet published, but Prof. Milnor has allowed
me to distribute the early version to you. The only condition is that
we provided him with suggestions, comments, and/or corrections.
We will also use parts of
However, you need not buy these books. I will put them on reserve in
the library. Other books that you might find interesting and/or useful are:
The main book we will use is a preprint version of
For background reading (ie targeted more towards advanced undergraduates),
- "Introduction to Dynamical Systems," M. Brin and G. Stuck, Cambridge
University Press 2002.
- "Introduction to the Modern Theory of Dynamical Systems,"
A. Katok and B. Hasselblatt, Cambridge University Press 1995.
introduction to ergodic theory," P. Walters, Springer-Verlag, 1982.
- "Topics from
One-Dimensional Dynamics," K. M. Brucks and H. Bruin, Cambridge University Press, 2004.
A .pdf file of the syllabus can be found here.
The basic plan for the course is:
Your grades will be based upon homework assignments (80%), given
approximately every one-two weeks and an end of the semester
presentation (20%) on a topic of your choice.
- Introduction: Continuous vs. discrete dynamics; First examples:
circle rotations and doubling map.
- Topological Dynamics
- Ergodic Thoery
- Hyperbolic Dynamics (for smooth maps)
- Circle Maps and Rotation Numbers (if time)
Instructor: Margaret Beck
Office: MCS 233
Email: mabeck -at- math.bu.edu
Office Hours: M 2:30-3:45 and W 12-1, or by appointment