Math 581BA: DYNAMICAL SYSTEMS
Boris Solomyak
Autumn 2004
The mathematical theory of dynamical systems studies the global orbit structure
of maps and flows. The field of dynamical systems comprises several
major disciplines, among them ergodic theory, symbolic dynamics,
topological dynamics, and differentiable dynamics. This course aims to give
a general introduction into the subject, rather than concentrating on one
of these areas.
- We will study discrete dynamical systems, that is, iteration of maps
(flows will be mentioned only in passing).
- We will follow, somewhat loosely, the encyclopedic monograph
``Introduction to the Modern Theory of Dynamical Systems'' by
A. Katok and B. Hasselblatt (Cambridge University Press, 1995), although we
will only be able to cover a small part of the book.
- Make sure you buy the latest, 4th printing of the book (available at the
U. Bookstore), since there are many typos and small errors in the 1st
1995 printing. If you have an older version, you can download the list of
corrections from the website http://www.tufts.edu/~bhasselb/thebook.html
- The approach is to introduce the principal notions and methods of
dynamics via a series of basic examples.
- Some of the highlights of the course: the Poincare and Denjoy theory
of circle homeomorphisms and diffeomorphisms, coding, horseshoes, and
Markov partitions, the Poincare-Siegel Theorem, and topological entropy.
- Homework will be assigned but not collected; it will be discussed
occasionally in class.
- Grades will be based on attendance and class participation