Main course literature:
Omri Sarig, Lecture Notes on Ergodic Theory.
Dave Witte Morris, Ratner's theorems on unipotent flows,
University of Chicago Press, 2005.
Marcelo Viana, Ergodic Theory of Interval Exchange Maps,
Rev. Mat. Complut. 19 (2006), 7-100.
Marcelo Viana, Lyapunov Exponents of Teichmüller flows,
in Partially hyperbolic dynamics, laminations, and Teichmüller flow,
Amer. Math. Soc., Providence, RI, 2007.
We will also work directly from some original research articles:
D. Ruelle, Bol. Soc. Brasil. Mat. 9 (1978), 83-87.
R. Mañé, Ergodic Theory Dynamical Systems 1 (1981), 95-102 (and errata).
Lectures: here.
Preliminary plan of lectures:
1. Introduction
2. Ergodic theorems
3. - // -
4. Ergodic decomposition
5. Introduction to homogeneous dynamics
6. The Subadditive Ergodic Theorem
7. The multiplicative ergodic theorem; Lyapunov exponents
8. - // -
9. Entropy
10. - // -
11. Pesin's entropy formula (following the papers by Ruelle and Mañé)
12. - // -
13. Interval Exchange Transformations;
Rauzy-Veech renormalization;
Teichmüller flow.
14. - // -
15. - // -
16. Translation surfaces.
17. - // -
18. Lyapunov exponents of Teichmüller flows.
Examination:
See here for a list of homework exercises.
Each participant taking the course for credit can choose the problems that interest him or her the most and hand in solutions to
these.
The condition for passing the course is to hand in acceptable solutions for problems for a total of at least "100 pt".
DEADLINE: On May 16 or earlier, please show me evidence that you have seriously started on
problems with a total value of at least 80 pt.
Andreas Strömbergsson, Tel. (018) 4713221, e-mail: astrombe@math.uu.se