C1 density of stable ergodicity

By Artur Avila, S. Crovisier, Amie Wilkinson. Advances in Mathematics, 2017

65 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e8546adc8a635d39e448a872f50a29c414e59120