Math 523 - Introduction to Ergodic Theory
|| meeting times
| Cupples I, 199
|| Tue Th 1:00 - 2:30 PM
|| phone #
|| office hours
| Renato Feres
|| Cupples I 17
|| Mon 4:00 - 5:00 PM / Tue 3:00 - 4:00 PM / Fri 2:00 - 3:00 PM
Note: You can see me outside the set office hours, but contact me in advance
to be sure I'm in.
Course Plan: We plan to cover elements of the theory of dynamical systems with emphasis on
ergodic theory. The following is a rough list of topics.
1. An assortment of examples and basic properties of dynamical systems;
2. Short review of measure theory and Hilbert spaces;
3. Invariant measures and recurrence;
4. The principal ergodic theorems;
5. Mixing properties;
6. Entropy theory;
7. Rudments of information theory;
8. Oseledec theorem and smooth ergodic theory;
Texts: the main text for the course is the first one in the below list. The other texts listed
should also be useful.
1. Topics in Ergodic Theory, by W. Parry. Cambridge Tracts in Mathematics, 75. Cambridge U. Press, 1981 (new edition 2004)
2. An Introduction to Ergodic Theory, by Peter Walters. Graduate Texts in Mathematics, Springer Verlag, 1982
3. Introduction to the modern theory of dynamical systems, by A. Katok and B. Hasselblatt. Cambridge U. Press, 1995
Grades: will be based on a moderate amount of homework assignments and/or lecture presentation.