SDG meeting: Andy Hammerlindl -- Lecture on "Ergodicity and Partial Hyperbolicity"

Lecture 2 - Ergodicity and partial hyperbolicity 

Globally hyperbolic systems (also called Anosov systems) are stably ergodic.  For
decades these were the only known examples of stable ergodicity.  This was unfortunate,
because Anosov systems are relatively rare.  Then, in 1994, Grayson, Pugh, and Shub
discovered a non-Anosov example.  Further examples were found, leading to the Pugh-Shub
conjectures, which state that stable ergodicity is dense among partially hyperbolic
systems, and that this ergodicity is due to a (slightly) technical condition called
“accessibility." 

In this talk, I’ll define partial hyperbolicity and accessibility and show how the proof
of ergodicity for Anosov systems can be extended, in some cases, to the partially
hyperbolic setting.