Elizabeth Burslem (Northwestern University)

Centralizers of partially hyperbolic diffeomorphisms.

Abstract. Smale has conjectured that the generic diffeomorphism of a compact manifold has trivial centralizer - i.e. commutes only with powers of itself. The conjecture is known to be true for diffeomorphisms of a circle, and for structurally stable diffeomorphisms. We look at the case of partially hyperbolic diffeomorphisms - in particular perturbations of the time-t map of an Anosov flow, and partially hyperbolic skew products and their perturbations.