Amie Wilkinson

Abstract:   Which diffeomorphisms of a compact manifold M commute with no other diffeomorphisms (except their own powers)? Smale asked if such highly asymmetrical diffeomorphisms are typical, in that they are dense in the C^r topology on the space of C^r diffeomorphisms Diff^r(M). In this talk I will explain the recent (positive) solution to Smale's question for C^1 symplectomorphisms and volume-preserving diffeomorphisms. I will also discuss progress on the general case. This is joint work with Christian Bonatti and Sylvain Crovisier.