Math 211a - Dynamical Systems

Information for students, Fall 2004

Class meets at: Goldsmith 101, MWTh 12 NOON - 1 PM
Lecturer: Dmitry Kleinbock
Office: Goldsmith 207, phone 6-3059
Office Hours: Th 2-3 or by appt.
E-mail address: kleinboc@brandeis.edu



Textbook: Introduction to Dynamical Systems, by Michael Brin and Garrett Stuck, Cambridge Univ. Press, 2002. It is on reserve at the Science Library. We will cover most of Chapters 1-4, and then decide what to do next based on the interest of participants.

Useful online sources are: lecture notes by Bryna Kra, and a book by Mark Pollicott and Michiko Yuri.

Links to some of the topics mentioned in class: Collatz Problem, cat map animation, solenoid animation, well-rounded lattices,
arithmetic progressions in primes, a book by Dave Morris on Ratner Theorem, with a chapter about entropy

Further reading: a long survey paper by Bergelson,
and two short unpublished drafts related to shrinking targets: by myself and Margulis and Fayad.



Students are expected to read the textbook and do homework (assigned each Wednesday and due the following Wednesday). The final grade will be based on homework and class participation. Assigned homework problems, posted below, will be of three types:

(easy): make sure you can do it and talk to me if you cannot; do not hand in

standard: work it out and hand in your solution

challenging: don't panic if you cannot do it, but if you can, hand in your solution for extra credit

Homework assignments and deadlines:

1 Problems (1.1.1-2), (1.2.1), 1.2.2-3, 1.2.4, (1.3.1), 1.3.2-3, (1.3.4), 1.3.5 September 15
2 Problems 1.4.1-2, (1.4.3-4), (1.6.1), 1.6.2, (1.6.3), (1.7.1-2), 1.7.3, 1.11.1, 1.11.3 September 22
3 Problems (2.1.1-5), 2.1.6, (2.1.7-8), 2.1.9-11 September 29
4 Problems (2.8.1-3), 2.8.4, and five more problems (pdf) October 13
5 Problems (2.2.1-3), 2.2.6, (2.3.1-4), and eight more problems (pdf) October 27
6 Problems (2.5.1-5), 2.5.6, (2.5.7), (2.6.1-2), (7.1.1-2), 7.1.3-4 and five more problems (pdf) November 10
7 Problems 4.1.1, (4.2.2), 4.2.3 and seven more problems (pdf) November 17
8 Problems (4.3.1), 4.3.2, 4.3.5, (4.3.6-7), (4.4.3-4), 4.5.1, 4.5.6, 4.6.3, (4.6.4), 4.6.5 December 2
9 Problems (9.1.1-3), 9.2.2, 9.3.1, (9.3.2), 9.3.4-7 December 9

Have a refreshing break and best wishes for 2005!