SDG meeting: Andy Hammerlindl -- Lecture on "Stable Ergodicity on Surfaces"

Lecture 1 - Stable ergodicity on surfaces 

The map A(x,y) = (2x+y, x+y) on the torus is ergodic.  That in itself is not overly
difficult to prove.  What’s more interesting is that the system is stably ergodic: every
area-preserving C^2 diffeomorphism close to A is also ergodic.  However, it is an open
question if every C^1 diffeomorphism near A is ergodic.  

I’ll give an outline of the proof of stable ergodicity for these types of systems and
show why the C^1 case is so different from the C^2 case.  

I’ll also talk about how, in some sense, every stably ergodic system on a surface has to
be a linear example like the map A defined above.