$C^1$ density of stable ergodicity Article - 2019

A. Avila, Sylvain Crovisier, A. Wilkinson

A. Avila, Sylvain Crovisier, A. Wilkinson, « $C^1$ density of stable ergodicity  », Advances in Math., à paraître

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.

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