MA771 - Discrete Dynamical Systems - Spring
Lectures: MWF 11:15-12:05 in MCS B23
Content of Course:
This course is a graduate level introduction to the mathematical theory of discrete dynamical
systems. The plan is to cover key topics from topological dynamics,
low-dimensional dynamics, hyperbolic dynamics, symbolic dynamics, and ergodic
theory, including fundamental examples such as circle rotations, expanding maps, shifts and subshifts,
quadratic maps, toral automorphisms, and horseshoes.
Your grade will be based entirely on homework assignments, which will be
assigned approximately every two weeks throughout the semester. Here is the syllabus.
- There will be no class or office hours on Mon 3/20 or Wed 3/22.
- HW 1, due Friday, Feb 10: On pages 24-25, please do 2.1-2.5, 2.8, 2.12, and 2.14
- HW 2, due Tuesday (which has a Monday schedule), Feb 21: On page 54,
please do 3.2, 3.4, and 3.6-3.8
- HW 3, due Friday, March 3: On pages 54-55, please do 3.9-3.13 and 3.16.
- HW 4, due Friday, March 24: On pages 84-85, please do 4.4, 4.5, 4.7-4.9,
- HW 5, due Wednesday, April 5: On pages 109-110, please do 5.2, 5.8, 5.9,
5.12, and 5.13.
- HW 6, due Wednesday, April 19: On pages 178-179, please do 7.1, 7.4, 7.11
(parts 2 and 3 only), 7.13, 7.15, and 7.16.
- HW 7, due Monday, May 1 (please put it in my maibox by 11:15am): On pages
200-202, please do 8.1, 8.4, 8.15, and 8.20 (part 1 only).
Books and references:
If you click on the above link and are on-campus (or logged into the campus
VPN), you should then be able to click on the "book" link and get a free .pdf
copy of the book.
The main book we will use is a
Other books you may find useful include
You don't need to buy any of these books. For background reading (ie targeted more towards advanced undergraduates),
- "Concepts and results in dynamical systems," P. Collet and
J.-P. Eckmann, Springer-Verlag 2006.
systems: stability, symbolic dynamics, and chaos," C. Robinson,
CRC Press, 1999.
- "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.
Instructor: Margaret Beck
Office: MCS 233
Email: mabeck -at- math.bu.edu
Office Hours: Mondays 2:30-3:30, Wednesdays 10-11, or by appointment