C1 density of stable ergodicity

Abstract

We prove a $C^1$ version of a conjecture by Pugh and Shub: among partially hyperbolic volume-preserving $C^r$ diffeomorphisms, r>1, the stably ergodic ones are $C^1$-dense. To establish these results, we develop new perturbation tools for the $C^1$ topology: linearization of horseshoes while preserving entropy, and creation of “superblenders” from hyperbolic sets with large entropy.