Introduction to the classical Multiplicative Ergodic Theorem

Dynamical Systems Working Seminar
Tuesday, July 21, 2020 - 12:00pm for 1 hour (actually 50 minutes)
Yuqing Lin – UT Austin –
Alex Blumenthal

Please Note: This is an expository talk, to be paired with the CDSNS Colloquium held the next day.

 This is a gentle introduction to the classical Oseledets' Multiplicative Ergodic Theorem (MET), which can be viewed as either a dynamical version of the Jordan normal form of a matrix, or a matrix version of the pointwise ergodic theorem (which itself can be viewed as a generalization of the strong law of large numbers).  We will also sketch Raghunathan's proof of the MET and discuss how the MET can be applied to smooth ergodic theory.