Topics in Ergodic Theory IV: Shannon-McMillan-Breiman Theorem.

Series: 
Dynamical Systems Working Seminar
Friday, March 28, 2014 - 13:05
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
Georgia Tech
We present the proof of the Shannon-McMillan-Breiman Theorem. This is part of a reading seminar geared towards understanding of Smooth Ergodic Theory. (The study of dynamical systems using at the same time tools from measure theory and from differential geometry)It should be accesible to graduate students and the presentation is informal. The first goal will be a proof of the Oseledets multiplicative ergodic theorem for random matrices. Then, we will try to cover the Pesin entropy formula, invariant manifolds, etc.