Math 523 - Introduction to Ergodic Theory

Fall 2006

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.