Type: Seminar

Distribution: World

Expiry: 11 Jun 2014

CalTitle1: SDG meeting: Andy Hammerlindl -- Lecture on "Stable Ergodicity"

Auth: gottwald@pgottwald2.pc (assumed)

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.