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Time: Wednesday/Friday 1:30pm-2:50pm
Location: Ryerson 358
NOTE
On Friday, 21 February, class will end at 2:25pm, due to D. Dolgopyat's lecture in the probability seminar.
Wednesday classes will now start at 1:35pm instead of 1:30pm, to allow students to attend Leonid Polterovich's class.


References

[Fr] Furman - Random walks on groups and random transformations
[EW] Einsiedler, Ward - Ergodic Theory with a view towards Number Theory
[MET] Lectures on the Oseledets Multiplicative Ergodic Theorem
The dynamics seminar meets on Mondays at 2:30pm, the schedule is here.


Schedule


Week Topic
8 - 10 Jan Introduction; Birkhoff & Kingman ergodic theorems
15 - 17 Jan Examples
22 - 24 Jan Factors, Furstenberg examples
29 - 31 Jan Hopf argument, Lyapunov exponents
5 - 7 Feb Positivity of top Lyapunov exponent
12 - 14 Feb Conditional expectation. More on random walks.
19 - 21 Feb Positivity and simplicity of top Lyapunov exponent
26 - 28 Feb Introduction to entropy
4 - 6 Mar Abelian dynamics on the circle
11 - 13 Mar Abelian dynamics on the space of lattices


Homework & Notes


The preliminary lecture notes below should be used with care; the notes are incomplete at the moment, several topics are missing. Please let me know if you spot any errors.
Homework problems are at the end of the Lecture Notes.