MA771 - Discrete Dynamical Systems - Spring 2010

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:

The main book we will use is a preprint version of

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: For background reading (ie targeted more towards advanced undergraduates), consult


A .pdf file of the syllabus can be found here. The basic plan for the course is:

  • 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)
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.

Contact Information

Instructor: Margaret Beck
Office: MCS 233
Phone: 617-358-3314
Email: mabeck -at-
Office Hours: M 2:30-3:45 and W 12-1, or by appointment